{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T11:31:33Z","timestamp":1774870293079,"version":"3.50.1"},"reference-count":118,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,3,19]],"date-time":"2013-03-19T00:00:00Z","timestamp":1363651200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2013,3,19]],"date-time":"2013-03-19T00:00:00Z","timestamp":1363651200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["fcaa"],"published-print":{"date-parts":[[2013,6]]},"DOI":"10.2478\/s13540-013-0030-y","type":"journal-article","created":{"date-parts":[[2013,3,18]],"date-time":"2013-03-18T16:50:47Z","timestamp":1363625447000},"page":"479-500","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":73,"title":["Science metrics on fractional calculus development since 1966"],"prefix":"10.1007","volume":"16","author":[{"given":"J.","family":"Tenreiro Machado","sequence":"first","affiliation":[]},{"given":"Alexandra M.","family":"Galhano","sequence":"additional","affiliation":[]},{"given":"Juan J.","family":"Trujillo","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2013,3,19]]},"reference":[{"key":"30_CR1","series-title":"Developments in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-4036-9","volume-title":"Topics in Fractional Differential Equations","author":"S Abbas","year":"2012","unstructured":"S. Abbas, M. Benchohra, G. M. N\u2019Gu\u00e9r\u00e9kata, Topics in Fractional Differential Equations, Developments in Mathematics, Vol. 27. Springer, New York (2012)."},{"key":"30_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-98128-4","volume-title":"Fractional Differentiation Inequalities","author":"G A Anastassiou","year":"2009","unstructured":"G. A. Anastassiou, Fractional Differentiation Inequalities. Springer, New York, Heidelberg (2009)."},{"key":"30_CR3","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-30898-7","volume-title":"q-Fractional Calculus and Euations","author":"M H Annaby","year":"2012","unstructured":"M. H. Annaby, Z.S. Mansour, q-Fractional Calculus and Euations, Lecture Notes in Mathematics, Vol. 2056. Springer, Heidelberg (2012)."},{"key":"30_CR4","volume-title":"Nonlinear Noninteger Order Systems: Theory and Applications, Nonlinear Science","author":"P Arena","year":"2001","unstructured":"P. Arena, R. Caponetto, M. Porto, L. Fortuna, Nonlinear Noninteger Order Systems: Theory and Applications, Nonlinear Science. World Scientific Publishing Company, Singapore (2001)."},{"key":"30_CR5","volume-title":"Some Results in Fractional Calculus","author":"S Al-Azawi","year":"2011","unstructured":"S. Al-Azawi, Some Results in Fractional Calculus. LAP Lambert Acad. Publ. (2011)."},{"key":"30_CR6","volume-title":"Turbulence and Diffusion: Scaling Versus Equations","author":"O G Bakunin","year":"2008","unstructured":"O. G. Bakunin, Turbulence and Diffusion: Scaling Versus Equations, Springer Series in Synergetics. Springer-Verlag, Berlin, Heidelberg (2008)."},{"key":"30_CR7","volume-title":"New Trends in Nanotechnology and Fractional Calculus Applications","year":"2010","unstructured":"D. Baleanu, Z.B. Guven\u00e7, J. Tenreiro Machado (Eds.), New Trends in Nanotechnology and Fractional Calculus Applications. Springer,, Dordrecht (2010)."},{"key":"30_CR8","volume-title":"Fractional Dynamics and Control","year":"2011","unstructured":"D. Baleanu, J.A. Tenreiro Machado, A.C.J. Luo (Eds.), Fractional Dynamics and Control. Springer, New York (2011)."},{"key":"30_CR9","doi-asserted-by":"crossref","DOI":"10.1142\/8180","volume-title":"Fractional Calculus: Models and Numerical Methods","author":"D Baleanu","year":"2012","unstructured":"D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus: Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos. World Scientific Publishing Company, Singapore (2012)."},{"key":"30_CR10","volume-title":"Handbook of Special Functions. Derivatives, Integrals, Series and Other Formulas","author":"Y A Brychkov","year":"2009","unstructured":"Y. A. Brychkov, Handbook of Special Functions. Derivatives, Integrals, Series and Other Formulas. Chapman and Hall\/CRC, Boca Raton (2009)."},{"key":"30_CR11","doi-asserted-by":"crossref","DOI":"10.1142\/7709","volume-title":"Fractional Order Systems: Modeling and Control Applications","author":"R Caponetto","year":"2010","unstructured":"R. Caponetto, G. Dongola, L. Fortuna, I. Petr\u00e1\u0161, Fractional Order Systems: Modeling and Control Applications. World Scientific,, Singapore (2010)."},{"key":"30_CR12","volume-title":"Elasticit\u00e1 e Dissipazione","author":"M Caputo","year":"1969","unstructured":"M. Caputo, Elasticit\u00e1 e Dissipazione. Zanichelli, Bologna (1969)."},{"key":"30_CR13","volume-title":"Lectures on^Seismology and Rheological Tectonics","author":"M Caputo","year":"1992","unstructured":"M. Caputo, Lectures on Seismology and Rheological Tectonics. Lecture Notes, Universit\u00e1 La Sapienza, Dipartimento di Fisica, Roma (1992)."},{"key":"30_CR14","volume-title":"Fractals and Fractional Calculus in Continuum Mechanics","year":"1997","unstructured":"A. Carpinteri, F. Mainardi (Eds.), Fractals and Fractional Calculus in Continuum Mechanics. (CISM International Centre for Mechanical Sciences), Springer, Wien (1997)."},{"key":"30_CR15","volume-title":"Functional Fractional Calculus for System Identification and Controls","author":"S Das","year":"2009","unstructured":"S. Das, Functional Fractional Calculus for System Identification and Controls. Springer-Verlag, Berlin, Heidelberg (2009)."},{"key":"30_CR16","series-title":"SpringerBriefs in Applied Sciences and Technology","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-23117-9","volume-title":"Fractional Order Signal Processing: Introductory Concepts and Applications","author":"S Das","year":"2012","unstructured":"S. Das, I. Pan, Fractional Order Signal Processing: Introductory Concepts and Applications, SpringerBriefs in Applied Sciences and Technology. Springer, Heidelberg (2012)."},{"key":"30_CR17","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type","author":"K Diethelm","year":"2010","unstructured":"K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics. Springer, Heidelberg (2010)."},{"key":"30_CR18","volume-title":"Les diff\u00e9rentielles m\u00e9taphysiques (histoire et philosophie de la g\u00e9n\u00e9ralisation de l\u2019ordre de d\u00e9rivation)","author":"S Dugowson","year":"1994","unstructured":"S. Dugowson, Les diff\u00e9rentielles m\u00e9taphysiques (histoire et philosophie de la g\u00e9n\u00e9ralisation de l\u2019ordre de d\u00e9rivation), PhD, Th\u00e8se. Universit\u00e9 Paris Nord, Paris, France (1994)."},{"key":"30_CR19","volume-title":"Integral Transforms and Representations of Functions in Complex Domain","author":"M M Dzherbashyan","year":"1966","unstructured":"M. M. Dzherbashyan, Integral Transforms and Representations of Functions in Complex Domain. Nauka, Moscow (1966), In Russian."},{"key":"30_CR20","volume-title":"Intelligent Systems at the Service of Mankind","year":"2005","unstructured":"W. Elmenreich, J. Tenreiro Machado, I.J. Rudas (Ed.), Intelligent Systems at the Service of Mankind, Vol. 2. Ubooks Verlag, Neus\u00e4ss (2005)."},{"key":"30_CR21","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/S0167-2789(01)00234-2","volume":"154","author":"R Ferrari","year":"2001","unstructured":"R. Ferrari, A.J. Manfroi, W.R. Young, Strongly and weakly self-similar diffusion. Physica D\n                           154 (2001) 111\u2013137.","journal-title":"Physica D"},{"key":"30_CR22","volume-title":"First annual report, NASA\/TM 2002-211914","author":"A Freed","year":"2002","unstructured":"A. Freed, K. Diethelm, Yu. Luchko, Fractional-order viscoelasticity (FOV): Constitutive development using the fractional calculus. First annual report, NASA\/TM 2002-211914, NASA\u2019s Glenn Research Center, Brook Rark, Ohio (2002)."},{"key":"30_CR23","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0084665","volume-title":"Abel Integral Equations: Analysis and Applications","author":"R Gorenflo","year":"1991","unstructured":"R. Gorenflo, S. Vessella, Abel Integral Equations: Analysis and Applications, Lecture Notes in Mathematics, Vol. 1461, Springer, Berlin (1991)."},{"key":"30_CR24","volume-title":"Proceedings of the Third UN\/ESA\/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science: National Astronomical Observatory of Japan","year":"2010","unstructured":"H. J. Haubold, A.M. Mathai (Ed.), Proceedings of the Third UN\/ESA\/NASA Workshop on the International Heliophysical Year 2007 and Basic Space Science: National Astronomical Observatory of Japan (Astrophysics and Space Science Proceedings). Springer, Berlin (2010)."},{"key":"30_CR25","doi-asserted-by":"publisher","DOI":"10.1142\/9789814340250","volume-title":"Fractional Calculus: An Introduction for Physicists","author":"R Herrmann","year":"2011","unstructured":"R. Herrmann, Fractional Calculus: An Introduction for Physicists, World Scientific Publishing Company, Singapore (2011)."},{"key":"30_CR26","volume-title":"Applications of Fractional Calculus in Physics","year":"2000","unstructured":"R. Hilfer (Ed.), Applications of Fractional Calculus in Physics. World Scientific Publishing Company, Singapore (2000)."},{"key":"30_CR27","doi-asserted-by":"crossref","DOI":"10.1142\/p264","volume-title":"Pseudo-Differential Operators and Markov Processes: Fourier Analysis and Semigroups","author":"N Jacob","year":"2002","unstructured":"N. Jacob, Pseudo-Differential Operators and Markov Processes: Fourier Analysis and Semigroups, Vol. 1. World Scientific Publishing Company, Singapore (2002)."},{"key":"30_CR28","doi-asserted-by":"publisher","DOI":"10.1142\/9781860949562","volume-title":"Pseudo Differential Operators & Markov Processes: Generators and Their Potential Theory","author":"N Jacob","year":"2002","unstructured":"N. Jacob, Pseudo Differential Operators & Markov Processes: Generators and Their Potential Theory, Vol. 2. World Scientific Publishing Company, Singapore (2002)."},{"key":"30_CR29","doi-asserted-by":"publisher","DOI":"10.1142\/9781860947155","volume-title":"Pseudo Differential Operators & Markov Processes: Markov Processes and Applications","author":"N Jacob","year":"2005","unstructured":"N. Jacob, Pseudo Differential Operators & Markov Processes: Markov Processes and Applications, Vol. 3. Imperial College Press, London (2005)."},{"key":"30_CR30","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-2852-6","volume-title":"Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives","author":"Z Jiao","year":"2012","unstructured":"Z. Jiao, Y. Q. Chen, I. Podlubny, Distributed-Order Dynamic Systems: Stability, Simulation, Applications and Perspectives. SpringerBriefs in Electrical and Computer Engineering, Springer, London (2012)."},{"key":"30_CR31","volume-title":"Recent Advances in Fractional Calculus","year":"1993","unstructured":"R. N. Kalia (Ed.), Recent Advances in Fractional Calculus, (Global Research Notes in Mathematics Ser.). Global Publ. Co, Minnesota (1993)."},{"key":"30_CR32","series-title":"Series on Analytic Methods and Special Functions","doi-asserted-by":"publisher","DOI":"10.1201\/9780203487372","volume-title":"H-Transforms: Theory and Applications","author":"A A Kilbas","year":"2004","unstructured":"A. A. Kilbas, M. Saigo, H-Transforms: Theory and Applications, Series on Analytic Methods and Special Functions, Vol. 9. CRC Press, Boca Raton (2004)."},{"key":"30_CR33","series-title":"North-Holland Mathematics Studies","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-0208(06)80001-0","volume-title":"Theory and Applications of Fractional Differential Equations","author":"A A Kilbas","year":"2006","unstructured":"A. A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204. Elsevier, Amsterdam (2006)."},{"key":"30_CR34","volume-title":"Analytic Methods of Analysis and Differential Equations: AMADE-2006","year":"2008","unstructured":"A. Kilbas, S. Rogosin (Eds.), Analytic Methods of Analysis and Differential Equations: AMADE-2006, Cambridge Scientific Publishers, Cambridge (2008)."},{"key":"30_CR35","volume-title":"Analytic Methods of Analysis and Differential Equations: AMADE 2009","year":"2012","unstructured":"A. A. Kilbas, S. V. Rogosin (Eds.), Analytic Methods of Analysis and Differential Equations: AMADE 2009. Cambridge Scientific Publishers, Cambridge (2012)."},{"key":"30_CR36","series-title":"Pitman Research Notes in Mathematics","volume-title":"Generalized Fractional Calculus and Applications","author":"V S Kiryakova","year":"1994","unstructured":"V. S. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics, Vol. 301, Longman Sci. Tech. & J. Wiley, New York (1994)."},{"key":"30_CR37","volume-title":"Fractional Dynamics: Recent Advances","year":"2011","unstructured":"J. Klafter, S.C. Lim, R. Metzler (Eds.), Fractional Dynamics: Recent Advances. World Scientific Publ. Co., Singapore (2011)."},{"key":"30_CR38","doi-asserted-by":"crossref","DOI":"10.1093\/acprof:oso\/9780199234868.001.0001","volume-title":"First Steps in Random Walks: From Tools to Applications","author":"J Klafter","year":"2011","unstructured":"J. Klafter, I.M. Sokolov, First Steps in Random Walks: From Tools to Applications. Oxford University Press, Oxford (2011)."},{"key":"30_CR39","volume-title":"Anomalous Transport: Foundations and Applications","year":"2008","unstructured":"R. Klages, G.R. Radons, I.M. Sokolov (Eds.), Anomalous Transport: Foundations and Applications. Wiley-VCH, Weinheim (2008)."},{"key":"30_CR40","volume-title":"On Solutions of Linear Fractional Differential Equations of a Variational Type","author":"M Klimek","year":"2009","unstructured":"M. Klimek, On Solutions of Linear Fractional Differential Equations of a Variational Type. Czestochowa University of Technology, Czestochowa (2009)."},{"key":"30_CR41","volume-title":"Theory of Fractional Dynamic Systems","author":"V Lakshmikantham","year":"2009","unstructured":"V. Lakshmikantham, S. Leela, J.V. Devi, Theory of Fractional Dynamic Systems. Cambridge Scientific Publishers, Cambridge (2009)."},{"key":"30_CR42","volume-title":"Fractional Differentiation and its Applications","year":"2005","unstructured":"A. Le M\u00e9haut\u00e9, J. Tenreiro Machado, J.C. Trigeassou, J. Sabatier (Eds.), Fractional Differentiation and its Applications. Ubooks Verlag, Neus\u00e4ss (2005)."},{"key":"30_CR43","volume-title":"An Introduction to Fractional Mechanics","author":"J S Leszczyanski","year":"2011","unstructured":"J. S. Leszczyanski, An Introduction to Fractional Mechanics. Czestochowa University of Technology, Czestochowa (2011)."},{"key":"30_CR44","volume-title":"Long-range Interaction, Stochasticity and Fractional Dynamics \u2014 Dedication to George M. Zaslavsky (1935\u20132008)","year":"2010","unstructured":"A. C.J. Luo, V.S. Afraimovich (Eds.), Long-range Interaction, Stochasticity and Fractional Dynamics \u2014 Dedication to George M. Zaslavsky (1935\u20132008). Higher Education Press and Springer, Beijing and Dordrecht (2010)."},{"issue":"12","key":"30_CR45","first-page":"317","volume":"16","author":"A J Lotka","year":"1926","unstructured":"A. J. Lotka, The frequency distribution of scientific productivity. Journal of the Washington Academy of Sciences\n                           16, No 12 (1926), 317\u2013324.","journal-title":"Journal of the Washington Academy of Sciences"},{"key":"30_CR46","volume-title":"Fractional Order Motion Controls","author":"Y C Ying Luo","year":"2012","unstructured":"Y. C. Ying Luo, Fractional Order Motion Controls. JohnWiley & Sons, New York (2012)."},{"issue":"3","key":"30_CR47","first-page":"329","volume":"13","author":"J Tenreiro Machado","year":"2010","unstructured":"J. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the recent history of fractional calculus. Fract. Calc. Appl. Anal. 13, No 3 (2010), 329\u2013334.","journal-title":"Fract. Calc. Appl. Anal"},{"issue":"4","key":"30_CR48","first-page":"447","volume":"13","author":"J A Tenreiro Machado","year":"2010","unstructured":"J. A. Tenreiro Machado, V. Kiryakova, F. Mainardi, A poster about the old history of fractional calculus. Fract. Calc. Appl. Anal. 13, No 4 (2010), 447\u2013454.","journal-title":"Fract. Calc. Appl. Anal"},{"issue":"3","key":"30_CR49","doi-asserted-by":"publisher","first-page":"1140","DOI":"10.1016\/j.cnsns.2010.05.027","volume":"16","author":"J Tenreiro Machado","year":"2011","unstructured":"J. Tenreiro Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus. Communications in Nonlinear Science and Numerical Simulations\n                           16, No 3 (2011), 1140\u20131153.","journal-title":"Communications in Nonlinear Science and Numerical Simulations"},{"key":"30_CR50","volume-title":"Nonlinear Science and Complexity","year":"2010","unstructured":"J. Tenreiro Machado, A.C.J. Luo, R.S. Barbosa, M.S. Silva, L.B. Figueiredo (Eds.), Nonlinear Science and Complexity. Springer, Dordrecht (2010)."},{"key":"30_CR51","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-8678-6","volume-title":"Intelligent Engineering Systems and Computational Cybernetics","author":"J Tenreiro Machado","year":"2009","unstructured":"J. Tenreiro Machado, B. Patk\u00e1i, I.J. Rudas (Eds.), Intelligent Engineering Systems and Computational Cybernetics. Springer, New York (2009)."},{"key":"30_CR52","volume-title":"Fractional Calculus in Bioengineering","author":"R L Magin","year":"2006","unstructured":"R. L. Magin, Fractional Calculus in Bioengineering. Begell House Inc., Redding, CT (2006)."},{"key":"30_CR53","doi-asserted-by":"publisher","DOI":"10.1142\/p614","volume-title":"Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models","author":"F Mainardi","year":"2010","unstructured":"F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models. Imperial College Press, London (2010)."},{"key":"30_CR54","doi-asserted-by":"crossref","DOI":"10.1142\/p871","volume-title":"Introduction to the Fractional Calculus of Variations","author":"A B Malinowska","year":"2012","unstructured":"A. B. Malinowska, D.F.M. Torres, Introduction to the Fractional Calculus of Variations. Imperial College Press, Singapore (2012)."},{"key":"30_CR55","volume-title":"Mathematics and Science Applications and Frontiers: With Fractional Calculus","author":"T Margulies","year":"2008","unstructured":"T. Margulies, Mathematics and Science Applications and Frontiers: With Fractional Calculus. Xlibris Corporation, USA (2008)."},{"key":"30_CR56","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0060468","volume-title":"Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences","author":"A M Mathai","year":"1973","unstructured":"A. M. Mathai, R.K. Saxena, Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, Lecture Notes in Mathematics. Springer, Heidelberg (1973)."},{"key":"30_CR57","volume-title":"The H-function with Applications in Statistics and Other Disciplines","author":"A M Mathai","year":"1978","unstructured":"A. M. Mathai, R.K. Saxena, The H-function with Applications in Statistics and Other Disciplines. Wiley Eastern Ltd, New Delhi (1978)."},{"key":"30_CR58","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75894-7","volume-title":"Special Functions for Applied Scientists","author":"A M Mathai","year":"2008","unstructured":"A. M. Mathai, H.J. Haubold, Special Functions for Applied Scientists. Springer, New York (2008)."},{"key":"30_CR59","volume-title":"The H-Function: Theory and Applications","author":"A M Mathai","year":"2009","unstructured":"A. M. Mathai, R.K. Saxena, H.J. Haubold, The H-Function: Theory and Applications. Springer, New York (2009)."},{"key":"30_CR60","volume-title":"Fractional Calculus and Integral Transforms of Generalized Functions","author":"A C McBride","year":"1979","unstructured":"A. C. McBride, Fractional Calculus and Integral Transforms of Generalized Functions. Pitman Press, San Francisco (1979)."},{"key":"30_CR61","series-title":"Research Notes in Mathematics","volume-title":"Fractional Calculus (Proc. of International Conference held in Ross Priory, University of Strathclyde, Scotland, August 1984)","year":"1985","unstructured":"A. C. McBride, G.F. Roach (Eds.), Fractional Calculus (Proc. of International Conference held in Ross Priory, University of Strathclyde, Scotland, August 1984). Research Notes in Mathematics No. 138, Pitman, London (1985)."},{"key":"30_CR62","series-title":"de Gruyter Studies in Mathematics","doi-asserted-by":"publisher","DOI":"10.1515\/9783110258165","volume-title":"Stochastic Models for Fractional Calculus","author":"M M Meerschaert","year":"2011","unstructured":"M. M. Meerschaert, A. Sikorskii, Stochastic Models for Fractional Calculus, de Gruyter Studies in Mathematics. Walter de Gruyter & Co, Berlin (2011)."},{"key":"30_CR63","volume-title":"Fl\u00e8ches du temps et g\u00e9om\u00e9trie fractale","author":"A Le M\u00e9haut\u00e9","year":"1998","unstructured":"A. Le M\u00e9haut\u00e9, R.R. Nigmatullin, L. Nivanen, Fl\u00e8ches du temps et g\u00e9om\u00e9trie fractale. Herm\u00e8s, Paris (1998)."},{"key":"30_CR64","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"K S Miller","year":"1993","unstructured":"K. S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations. John Wiley and Sons, New York (1993)."},{"key":"30_CR65","series-title":"Series Advances in Industrial Control","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-84996-335-0","volume-title":"Fractionalorder Systems and Controls","author":"C A Monje","year":"2010","unstructured":"C. A. Monje, Y.Q. Chen, B.M. Vinagre, D. Xue, V. Feliu, Fractionalorder Systems and Controls, Series Advances in Industrial Control. Springer, London (2010)."},{"issue":"8","key":"30_CR66","first-page":"114","volume":"38","author":"G E Moore","year":"1965","unstructured":"G. E. Moore, Cramming more components onto integrated circuits. Electronics\n                           38, No 8 (1965), 114\u2013117.","journal-title":"Electronics"},{"key":"30_CR67","volume-title":"Fractional^Calculus and its Applications","author":"A M Nakhushev","year":"2003","unstructured":"A. M. Nakhushev, Fractional Calculus and its Applications. Fizmatlit, Moscow (2003), In Russian."},{"key":"30_CR68","volume-title":"Fractional Calculus","author":"K Nishimoto","year":"1984","unstructured":"K. Nishimoto, Fractional Calculus, Vol. 1. Descartes Press, Koriyama (1984)."},{"key":"30_CR69","volume-title":"Fractional Calculus, Vol. 2","author":"K Nishimoto","year":"1987","unstructured":"K. Nishimoto, Fractional Calculus, Vol. 2. Descartes Press, Koriyama (1987)."},{"key":"30_CR70","volume-title":"Fractional Calculus, Vol. 3","author":"K Nishimoto","year":"1989","unstructured":"K. Nishimoto, Fractional Calculus, Vol. 3. Descartes Press, Koriyama (1989)."},{"key":"30_CR71","volume-title":"Fractional Calculus, Vol. 4","author":"K Nishimoto","year":"1991","unstructured":"K. Nishimoto, Fractional Calculus, Vol. 4. Descartes Press, Koriyama (1991)."},{"key":"30_CR72","volume-title":"An Essence of Nishimoto\u2019s Fractional Calculus (Calculus of the 21st Century), Integrals and Differentiations of Arbitrary Order","author":"K Nishimoto","year":"1991","unstructured":"K. Nishimoto, An Essence of Nishimoto\u2019s Fractional Calculus (Calculus of the 21st Century), Integrals and Differentiations of Arbitrary Order. Descartes Press, Koriyama (1991)."},{"key":"30_CR73","volume-title":"Fractional Calculus, Vol. 5","author":"K Nishimoto","year":"1996","unstructured":"K. Nishimoto, Fractional Calculus, Vol. 5. Descartes Press, Koriyama (1996)."},{"key":"30_CR74","series-title":"Bocconi & Springer Series","doi-asserted-by":"publisher","DOI":"10.1007\/978-88-470-2823-4","volume-title":"Selected Aspects of Fractional Brownian Motion","author":"I Nourdin","year":"2012","unstructured":"I. Nourdin, Selected Aspects of Fractional Brownian Motion, Bocconi & Springer Series. Springer, Milano (2012)."},{"key":"30_CR75","volume-title":"The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order","author":"K B Oldham","year":"1974","unstructured":"K. B. Oldham, J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. Academic Press, New York (1974)."},{"key":"30_CR76","series-title":"Lecture Notes in Electrical Engineering","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-0747-4","volume-title":"Fractional Calculus for Scientists and Engineers","author":"M D Ortigueira","year":"2011","unstructured":"M. D. Ortigueira, Fractional Calculus for Scientists and Engineers, Lecture Notes in Electrical Engineering. Springer, Dordrecht, Heidelberg (2011)."},{"key":"30_CR77","series-title":"Serie Automatique","volume-title":"Syst`emes asservis lin\u00e9aires d\u2019ordre fractionnaire: Th\u00e9orie et pratique","author":"A Oustaloup","year":"1983","unstructured":"A. Oustaloup, Syst`emes asservis lin\u00e9aires d\u2019ordre fractionnaire: Th\u00e9orie et pratique, Serie Automatique. Masson, Paris (1983)."},{"key":"30_CR78","volume-title":"La Commande CRONE: Commande Robuste d\u2019Ordre Non Entier","author":"A Oustaloup","year":"1991","unstructured":"A. Oustaloup, La Commande CRONE: Commande Robuste d\u2019Ordre Non Entier. Herm\u00e8s, Paris (1991)."},{"key":"30_CR79","volume-title":"La D\u00e9rivation Non Enti\u00e8re. Th\u00e9orie, Synth\u00e8se et Applications","author":"A Oustaloup","year":"1995","unstructured":"A. Oustaloup, La D\u00e9rivation Non Enti\u00e8re. Th\u00e9orie, Synth\u00e8se et Applications. Herm\u00e8s Science, Paris (1995)."},{"key":"30_CR80","volume-title":"La commande CRONE: du scalaire au multivariable","author":"A Oustaloup","year":"1999","unstructured":"A. Oustaloup, B. Mathieu, La commande CRONE: du scalaire au multivariable. Herm\u00e8s Science, Paris (1999)."},{"key":"30_CR81","volume-title":"C\u00e1lculo Fraccionario y Ecuaciones Diferenciales Fraccionarias","author":"B B Paz","year":"2003","unstructured":"B. B. Paz, A.A. Kilbas, J.J. Trujillo, C\u00e1lculo Fraccionario y Ecuaciones Diferenciales Fraccionarias. Universidad Nacional de Educaci\u00f3n a Distancia, UNED, Ediciones, Madrid (2003)."},{"key":"30_CR82","volume-title":"Analogue Realization of Fractional Order Controllers","author":"I Petras","year":"2002","unstructured":"I. Petras, I. Podlubny, P. O\u2019Leary, L. Dorcak, B. Vinagre, Analogue Realization of Fractional Order Controllers. FBERG, Technical University of Kosice, Kosice (2002)."},{"key":"30_CR83","series-title":"Series Nonlinear Physical Science","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-18101-6","volume-title":"Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation","author":"I Petr\u00e1\u0161","year":"2011","unstructured":"I. Petr\u00e1\u0161, Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation,, Series Nonlinear Physical Science, Springer, Heidelberg (2011)."},{"key":"30_CR84","series-title":"Mathematics in Science and Engineering","volume-title":"Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution","author":"I Podlubny","year":"1999","unstructured":"I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution, Mathematics in Science and Engineering, Vol. 198. Academic Press, San Diego (1999)."},{"key":"30_CR85","volume-title":"Integrals and Series, Vol. 3: More Special Functions","author":"A P Prudnikov","year":"1986","unstructured":"A. P. Prudnikov, Yu.A. Brychkov, O.I. Marichev, Integrals and Series, Vol. 3: More Special Functions. Nauka, Moscow (1986), In Russian."},{"key":"30_CR86","volume-title":"Partial Differential Equations of Fractional Order","author":"A V Pskhu","year":"2005","unstructured":"A. V. Pskhu, Partial Differential Equations of Fractional Order. Nauka, Moscow (2005), In Russian."},{"key":"30_CR87","volume-title":"Elements of Hereditary Solids Mechanics","author":"Y N Rabotnov","year":"1977","unstructured":"Y. N. Rabotnov, Elements of Hereditary Solids Mechanics. Nauka, Moscow (1977), In Russian."},{"key":"30_CR88","doi-asserted-by":"publisher","DOI":"10.1002\/9780470667125","volume-title":"Statistical Inference for Fractional Diffusion^Processes","author":"B L S P Rao","year":"2010","unstructured":"B. L. S. P. Rao, Statistical Inference for Fractional Diffusion Processes, Wiley Series in Probability and Statistics. Wiley, Chichester (2010)."},{"key":"30_CR89","volume-title":"Advances in Applied Analysis (Trends in Mathematics)","year":"2012","unstructured":"S. V. Rogosin, A. A. Koroleva (Eds.), Advances in Applied Analysis (Trends in Mathematics). Birkh\u00e4user, Basel (2012)."},{"key":"30_CR90","volume-title":"Fractional Calculus and Its Applications","year":"1974","unstructured":"B. Ross (Ed.), Fractional Calculus and Its Applications, Proc. of the International Conference, New Haven. Springer-Verlag, New York (1974)."},{"key":"30_CR91","series-title":"Pitman Monographs and Surveys in Pure and Applied Mathematics","volume-title":"Fractional Integrals and Potentials","author":"B Rubin","year":"1996","unstructured":"B. Rubin, Fractional Integrals and Potentials, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 82. Longman Sci. Techn. \/ CRC, Harlow (1996)."},{"key":"30_CR92","volume-title":"Transform Methods & Special Functions, Sofia\u20191994","year":"1995","unstructured":"P. Rusev, I. Dimovski, V. Kiryakova (Eds.), Transform Methods & Special Functions, Sofia\u20191994 (Proc. 1st Intern. Workshop, with Special Session on FC). Science Culture Technology Publishing (SCTP), Singapore (1995)."},{"key":"30_CR93","volume-title":"Transform Methods & Special Functions, Varna\u201996","year":"1998","unstructured":"P. Rusev, I. Dimovski, V. Kiryakova (Eds.), Transform Methods & Special Functions, Varna\u201996 (Proc. 2nd International Workshop, with Special Session on FC and \u201cOpen Problems in FC\u201d Round Table). Institute of Mathematics and Informatics (IMI \u2014 BAS), Sofia (1998)."},{"key":"30_CR94","volume-title":"Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering","year":"2007","unstructured":"J. Sabatier, O. P. Agrawal, J. Tenreiro Machado (Eds.), Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht (2007)."},{"key":"30_CR95","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"S G Samko","year":"1987","unstructured":"S. G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Nauka i Tekhnika, Minsk (1987)."},{"key":"30_CR96","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"S G Samko","year":"1993","unstructured":"S. G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, Yverdon (1993)."},{"key":"30_CR97","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4471-2233-3","volume-title":"Fractional^Processes and Fractional-Order Signal Processing: Techniques and Applications, Signals and Communication Technology","author":"H Sheng","year":"2012","unstructured":"H. Sheng, Y.Q. Chen, T. Qiu, Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications, Signals and Communication Technology. Springer, London (2012)."},{"key":"30_CR98","first-page":"487","volume":"11","author":"Z K Silagadze","year":"1997","unstructured":"Z. K. Silagadze, Citations and the Zipf-Mandelbrot\u2019s law. Complex Systems\n                           11 (1997), 487\u2013499.","journal-title":"Complex Systems"},{"key":"30_CR99","series-title":"Appl. Math. Series","volume-title":"The Use of Operators of Fractional Integration in Applied Mathematics","author":"I N Sneddon","year":"1979","unstructured":"I. N. Sneddon, The Use of Operators of Fractional Integration in Applied Mathematics, Appl. Math. Series. PWN-Polish Scientific Publishers, Warszawa-Poznan (1979)."},{"key":"30_CR100","volume-title":"The H-Functions of One and Two Variables with Applications","author":"S G H M Srivastava","year":"1982","unstructured":"S. G. H. M. Srivastava, K.C. Gupta, The H-Functions of One and Two Variables with Applications. South Asian Publishers, New Delhi and Madras (1982)."},{"key":"30_CR101","volume-title":"Univalent Functions, Fractional Calculus and Their Applications","year":"1990","unstructured":"H. M. Srivastava, O. Shigeyoshi (Eds.), Univalent Functions, Fractional Calculus and Their Applications. Ellis Horwood Ltd, Chichester (1990)."},{"key":"30_CR102","series-title":"Kluwer Series on Mathematics and Its Applications","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-015-8092-2","volume-title":"Theory and Applications of Convolution Integral Equations","author":"H M Srivastava","year":"1992","unstructured":"H. M. Srivastava, R. G. Buschman, Theory and Applications of Convolution Integral Equations. Kluwer Series on Mathematics and Its Applications, Vol. 79. Kluwer Academic Publishers, Dordrecht, Boston, and London (1992)."},{"key":"30_CR103","series-title":"Nonlinear Physical Science","volume-title":"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media","author":"V E Tarasov","year":"2011","unstructured":"V. E. Tarasov, Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media, Nonlinear Physical Science. Springer, Beijing, Heidelberg (2011)."},{"key":"30_CR104","volume-title":"Mathematical Methods in Engineering","year":"2007","unstructured":"K. Tas, J. Tenreiro Machado, D. Baleanu (Eds.), Mathematical Methods in Engineering. Springer, Dordrecht (2007)."},{"key":"30_CR105","series-title":"Series Modern Probability and Statistics","doi-asserted-by":"publisher","DOI":"10.1515\/9783110935974","volume-title":"Chance and Stability. Stable Distributions and their Applications","author":"V V Uchaikin","year":"1999","unstructured":"V. V. Uchaikin, V.M. Zolotarev, Chance and Stability. Stable Distributions and their Applications, Series Modern Probability and Statistics, No 3. VSP, Utrecht (1999)."},{"key":"30_CR106","volume-title":"Method of Fractional Derivatives","author":"V V Uchaikin","year":"2008","unstructured":"V. V. Uchaikin, Method of Fractional Derivatives. Artishok-Press, Ulyanovsk (2008), In Russian."},{"key":"30_CR107","doi-asserted-by":"crossref","DOI":"10.1049\/PBCE091E","volume-title":"An Introduction to Fractional Control","author":"D Val\u00e9rio","year":"2012","unstructured":"D. Val\u00e9rio, J.S. da Costa, An Introduction to Fractional Control. IET, Stevenage (2012)."},{"key":"30_CR108","volume-title":"Fractional Calculus and Approximation Methods in Modelling of Dynamic Systems","author":"V V Vasilyev","year":"2008","unstructured":"V. V. Vasilyev, L.A. Simak, Fractional Calculus and Approximation Methods in Modelling of Dynamic Systems. NAS (Nat. Acad. Sci.) of Ukraine, Academic Press, Kiev (2008)."},{"key":"30_CR109","series-title":"Studies of Nonlinear Phenomena in Life Sciences","doi-asserted-by":"publisher","DOI":"10.1142\/4069","volume-title":"Promiscuity, and Prophecy at the Millennium: A Tale of Tails (Studies of Nonlinear Phenomena in Life Science)","author":"B J West","year":"1999","unstructured":"B. J. West, Physiology, Promiscuity, and Prophecy at the Millennium: A Tale of Tails (Studies of Nonlinear Phenomena in Life Science), Studies of Nonlinear Phenomena in Life Sciences, Vol. 8. World Scientific Publishing Company, Singapore (1999)."},{"key":"30_CR110","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-21746-8","volume-title":"Physics of Fractal Operators","author":"B West","year":"2003","unstructured":"B. West, M. Bologna, P. Grigolini, Physics of Fractal Operators. Springer, New York (2003)."},{"key":"30_CR111","volume-title":"Dead Matter has Memory","author":"S Westerlund","year":"2002","unstructured":"S. Westerlund, Dead Matter has Memory!. Causal Consulting, Kalmar, Sweden (2002)."},{"key":"30_CR112","volume-title":"Linear Feedback Control:^Analysis and Design with MATLAB","author":"D Xue","year":"2008","unstructured":"D. Xue, Y.Q. Chen, D.P. Atherton, Linear Feedback Control: Analysis and Design with MATLAB. Society for Industrial Mathematics, Philadelphia (2008)."},{"key":"30_CR113","doi-asserted-by":"crossref","DOI":"10.1201\/b17177","volume-title":"Solving Applied Mathematical Problems with MATLAB","author":"D Xue","year":"2008","unstructured":"D. Xue, Y.Q. Chen, Solving Applied Mathematical Problems with MATLAB. Chapman & Hall\/CRC Press, Boca Raton (2008)."},{"key":"30_CR114","series-title":"Ser. Mathematics and Its Applications","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-1196-6","volume-title":"The Hypergeometric Approach to Integral Transforms and Convolutions","author":"S B Yakubovich","year":"1994","unstructured":"S. B. Yakubovich, Y.F. Luchko, The Hypergeometric Approach to Integral Transforms and Convolutions, Ser. Mathematics and Its Applications, Vol. 287. Kluwer Academic Publishers, Dordrecht, Boston, London (1994)."},{"key":"30_CR115","volume-title":"Local Fractional Functional^Analysis and Its Applications","author":"X J Yang","year":"2011","unstructured":"X. J. Yang, Local Fractional Functional Analysis and Its Applications. Asian Academic Publisher Limited, Hong Kong (2011)."},{"key":"30_CR116","volume-title":"Advanced Local Fractional^Calculus and Its Applications","author":"X J Yang","year":"2012","unstructured":"X. J. Yang, Advanced Local Fractional Calculus and Its Applications. World Science Publisher, New York (2012)."},{"key":"30_CR117","volume-title":"Hamiltonian Chaos and Fractional Dynamics","author":"G M Zaslavsky","year":"2008","unstructured":"G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics. Oxford University Press, Oxford (2008)."},{"key":"30_CR118","series-title":"SpringerBriefs in Applied Sciences and Technology","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-25358-4","volume-title":"Electromagnetic Fields and Waves in Fractional Dimensional Space","author":"M Zubair","year":"2012","unstructured":"M. Zubair, M.J. Mughal, Q.A. Naqvi, Electromagnetic Fields and Waves in Fractional Dimensional Space, SpringerBriefs in Applied Sciences and Technology. Springer, Heidelberg (2012)."}],"container-title":["Fractional Calculus and Applied Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.2478\/s13540-013-0030-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.2478\/s13540-013-0030-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s13540-013-0030-y\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.2478\/s13540-013-0030-y\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.2478\/s13540-013-0030-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,20]],"date-time":"2022-06-20T05:14:23Z","timestamp":1655702063000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.2478\/s13540-013-0030-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,19]]},"references-count":118,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2013,6]]}},"alternative-id":["30"],"URL":"https:\/\/doi.org\/10.2478\/s13540-013-0030-y","relation":{},"ISSN":["1311-0454","1314-2224"],"issn-type":[{"value":"1311-0454","type":"print"},{"value":"1314-2224","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3,19]]},"assertion":[{"value":"1 February 2013","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2013","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}