{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T18:33:42Z","timestamp":1772303622567,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T00:00:00Z","timestamp":1316044800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Nonlinear Dyn"],"published-print":{"date-parts":[[2012,4]]},"DOI":"10.1007\/s11071-011-0207-z","type":"journal-article","created":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T03:41:34Z","timestamp":1316058094000},"page":"107-115","source":"Crossref","is-referenced-by-count":102,"title":["Fractional order inductive phenomena based on the skin effect"],"prefix":"10.1007","volume":"68","author":[{"given":"J. A.","family":"Tenreiro Machado","sequence":"first","affiliation":[]},{"given":"Alexandra M. S. F.","family":"Galhano","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2011,9,15]]},"reference":[{"key":"207_CR1","series-title":"North-Holland Mathematics Studies","volume-title":"Theory and Applications of Fractional Differential Equations","author":"A.A. Kilbas","year":"2006","unstructured":"Kilbas, A.A., Srivastava, H.M., Trujillo, J.J.: Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, vol.\u00a0204. Elsevier, Amsterdam (2006)"},{"key":"207_CR2","first-page":"400","volume-title":"Proc. 1st IFAC Workshop on Fractional Differentiation and Its Applications","author":"A. Benchellal","year":"2004","unstructured":"Benchellal, A., Poinot, T., Bachir, S., Trigeassou, J.C.: Identification of a non-integer model of induction machines. In: Proc. 1st IFAC Workshop on Fractional Differentiation and Its Applications, Bordeaux, France, pp. 400\u2013407 (2004)"},{"key":"207_CR3","volume-title":"Applied Electricity for Engineers","author":"L. Bessonov","year":"1968","unstructured":"Bessonov, L.: Applied Electricity for Engineers. MIR Publishers, Moscow (1968)"},{"key":"207_CR4","first-page":"55","volume-title":"ESAIM Proceedings","author":"P. Bidan","year":"1998","unstructured":"Bidan, P.: Commande diffusive d\u2019une machine electrique: une introduction. In: ESAIM Proceedings, France, vol. 5, pp. 55\u201368 (1998)"},{"key":"207_CR5","volume-title":"Proc. of the 41st IEEE Int. Conf. on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics","author":"G.W. Bohannan","year":"2002","unstructured":"Bohannan, G.W.: Analog realization of a fractional control element\u2014revisited. In: Proc. of the 41st IEEE Int. Conf. on Decision and Control, Tutorial Workshop 2: Fractional Calculus Applications in Automatic Control and Robotics, Las Vegas, NV (2002)"},{"issue":"2","key":"207_CR6","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1109\/TCT.1964.1082270","volume":"CT-10","author":"G.E. Carlson","year":"1964","unstructured":"Carlson, G.E., Halijak, C.A.: Approximation of fractional capacitors (1\/s)(1\/n) by a regular newton process. IEEE Trans. Circuit Theory CT-10(2), 210\u2013213 (1964)","journal-title":"IEEE Trans. Circuit Theory"},{"key":"207_CR7","volume-title":"Genetic Algorithms in Search Optimization, and Machine Learning","author":"D.E. Goldenberg","year":"1989","unstructured":"Goldenberg, D.E.: Genetic Algorithms in Search Optimization, and Machine Learning. Addison-Wesley, Reading (1989)"},{"key":"207_CR8","volume-title":"Adaptation in Natural and Artificial Systems","author":"J.H. Holland","year":"1975","unstructured":"Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)"},{"key":"207_CR9","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/978-1-4020-6042-7_22","volume-title":"Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering","author":"J.A. Tenreiro Machado","year":"2007","unstructured":"Tenreiro Machado, J.A., Galhano, A., Boaventura, G.J., Jesus, I.S.: Fractional calculus analysis of the electrical skin phenomena. In: Sabatier, J., Agrawal, O.P., Tenreiro Machado, J. (eds.) Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, pp. 323\u2013332. Springer, Dordrecht (2007)"},{"issue":"3","key":"207_CR10","doi-asserted-by":"crossref","first-page":"482","DOI":"10.1016\/j.cnsns.2009.04.030","volume":"15","author":"J.A. Tenreiro Machado","year":"2010","unstructured":"Tenreiro Machado, J.A., Alexandra, A.M.O., Galhano, M., Tar, J.K.: Optimal approximation of fractional derivatives through discrete-time fractions using genetic algorithms. Commun. Nonlinear Sci. Numer. Simul. 15(3), 482\u2013490 (2010)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"issue":"1\u20132","key":"207_CR11","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s11071-008-9377-8","volume":"56","author":"I.S. Jesus","year":"2009","unstructured":"Jesus, I.S., Machado Tenreiro, J.A.: Development of fractional order capacitors based on electrolyte processes. Nonlinear Dyn. 56(1\u20132), 45\u201355 (2009)","journal-title":"Nonlinear Dyn."},{"key":"207_CR12","volume-title":"Einf\u00fchrung in die Theoretische Elektrotechnik","author":"K. K\u00fcpfm\u00fcller","year":"1939","unstructured":"K\u00fcpfm\u00fcller, K.: Einf\u00fchrung in die Theoretische Elektrotechnik. Springer, Berlin (1939)"},{"issue":"4","key":"207_CR13","first-page":"403","volume":"7","author":"J.A.T. Machado","year":"2004","unstructured":"Machado, J.A.T., Jesus, I.S.: A suggestion from the past? Fract. Calc. Appl. Anal. 7(4), 403\u2013407 (2004)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"207_CR14","first-page":"408","volume-title":"Proc. 1st IFAC Workshop on Fractional Differentiation and Its Applications","author":"W.A. Malpica","year":"2004","unstructured":"Malpica, W.A., Tenreiro Machado, J., Silva, J.F., de Barros, M.T.C.: Fractional order calculus on the estimation of short-circuit impedance of power transformers. In: Proc. 1st IFAC Workshop on Fractional Differentiation and Its Applications, Bordeaux, France, pp. 408\u2013415 (2004)"},{"key":"207_CR15","volume-title":"An Introduction to the Fractional Calculus and Fractional Differential Equations","author":"K.S. Miller","year":"1993","unstructured":"Miller, K.S., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York (1993)"},{"key":"207_CR16","volume-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"A. Milton","year":"1965","unstructured":"Milton, A., Stegun, I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1965)"},{"key":"207_CR17","volume-title":"The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order","author":"K.B. Oldham","year":"1974","unstructured":"Oldham, K.B., Spanier, J.: The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. Academic Press, New York (1974)"},{"key":"207_CR18","series-title":"An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution. Mathematics in Science and Engineering","volume-title":"Fractional Differential Equations","author":"I. Podlubny","year":"1998","unstructured":"Podlubny, I.: Fractional Differential Equations. An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution. Mathematics in Science and Engineering, vol.\u00a0198. Academic Press, San Diego (1998)"},{"key":"207_CR19","volume-title":"The Feynman Lectures on Physics: Mainly Electromagnetism and Matter","author":"P. Richard","year":"1964","unstructured":"Richard, P., Feynman, R.B.L., Sands, M.: The Feynman Lectures on Physics: Mainly Electromagnetism and Matter. Addison-Wesley, Reading (1964)"},{"key":"207_CR20","volume-title":"Fractional Integrals and Derivatives: Theory and Applications","author":"S.G. Samko","year":"1993","unstructured":"Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Amsterdam (1993)"},{"key":"207_CR21","volume-title":"Proc. of the ASME 2003 Design Engineering Technical Conf. and Computers and Information in Engineering Conf.","author":"C. Sylvain","year":"2003","unstructured":"Sylvain, C., Faucher, J.: Fractional order: Frequential parametric identification of the skin effect in the rotor bar of squirrel cage induction machine. In: Proc. of the ASME 2003 Design Engineering Technical Conf. and Computers and Information in Engineering Conf., Chicago, IL, DETC 2003\/VIB-48393 (2003)"},{"issue":"5","key":"207_CR22","doi-asserted-by":"crossref","first-page":"826","DOI":"10.1109\/94.326654","volume":"1","author":"S. Westerlund","year":"1994","unstructured":"Westerlund, S., Ekstam, L.: Capacitor theory. IEEE Trans. Dielectr. Electr. Insul. 1(5), 826\u2013839 (1994)","journal-title":"IEEE Trans. Dielectr. Electr. Insul."}],"container-title":["Nonlinear Dynamics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-011-0207-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11071-011-0207-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11071-011-0207-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T04:54:06Z","timestamp":1559364846000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11071-011-0207-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,15]]},"references-count":22,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2012,4]]}},"alternative-id":["207"],"URL":"https:\/\/doi.org\/10.1007\/s11071-011-0207-z","relation":{},"ISSN":["0924-090X","1573-269X"],"issn-type":[{"value":"0924-090X","type":"print"},{"value":"1573-269X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,15]]}}}