{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,18]],"date-time":"2025-05-18T18:20:57Z","timestamp":1747592457241},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T00:00:00Z","timestamp":1350604800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Optim Theory Appl"],"published-print":{"date-parts":[[2013,1]]},"DOI":"10.1007\/s10957-012-0203-6","type":"journal-article","created":{"date-parts":[[2012,10,19]],"date-time":"2012-10-19T00:45:46Z","timestamp":1350607546000},"page":"56-67","source":"Crossref","is-referenced-by-count":17,"title":["The DuBois\u2013Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler\u2013Lagrange Equation Involving Only Derivatives of Caputo"],"prefix":"10.1007","volume":"156","author":[{"given":"Matheus J.","family":"Lazo","sequence":"first","affiliation":[]},{"given":"Delfim F. M.","family":"Torres","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2012,10,19]]},"reference":[{"key":"203_CR1","volume-title":"The Fractional Calculus","author":"K.B. Oldham","year":"1974","unstructured":"Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)"},{"key":"203_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4020-6042-7","volume-title":"Advances in Fractional Calculus","author":"J. Sabatier","year":"2007","unstructured":"Sabatier, J., Agrawal, O.P., Tenreiro\u00a0Machado, J.A.: Advances in Fractional Calculus. Springer, Dordrecht (2007)"},{"key":"203_CR3","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. 204. Elsevier, Amsterdam (2006)"},{"key":"203_CR4","doi-asserted-by":"crossref","DOI":"10.1142\/3779","volume-title":"Applications of Fractional Calculus in Physics","author":"R. Hilfer","year":"2000","unstructured":"Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, River Edge (2000)"},{"key":"203_CR5","volume-title":"Fractional Calculus in Bioengineering","author":"R.L. Magin","year":"2006","unstructured":"Magin, R.L.: Fractional Calculus in Bioengineering. Begell House Publishers, Redding (2006)"},{"key":"203_CR6","doi-asserted-by":"crossref","DOI":"10.1142\/8072","volume-title":"Fractional Calculus: an Introduction for Physicists","author":"R. Herrmann","year":"2011","unstructured":"Herrmann, R.: Fractional Calculus: an Introduction for Physicists. World Scientific, Singapore (2011)"},{"key":"203_CR7","doi-asserted-by":"crossref","first-page":"R161","DOI":"10.1088\/0305-4470\/37\/31\/R01","volume":"37","author":"R. Metzler","year":"2004","unstructured":"Metzler, R., Klafter, J.: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A 37, R161\u2013R208 (2004)","journal-title":"J. Phys. A"},{"key":"203_CR8","volume-title":"Anomalous Transport: Foundations and Applications","author":"R. Klages","year":"2007","unstructured":"Klages, R., Radons, G., Sokolov, I.M.: Anomalous Transport: Foundations and Applications. VCH, Weinheim (2007)"},{"key":"203_CR9","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.66.056108","volume":"66","author":"N. Laskin","year":"2002","unstructured":"Laskin, N.: Fractional Schr\u00f6dinger equation. Phys. Rev. E 66, 056108 (2002), 7\u00a0pp.","journal-title":"Phys. Rev. E"},{"key":"203_CR10","doi-asserted-by":"crossref","first-page":"3339","DOI":"10.1063\/1.1769611","volume":"45","author":"M. Naber","year":"2004","unstructured":"Naber, M.: Time fractional Schr\u00f6dinger equation. J. Math. Phys. 45, 3339\u20133352 (2004)","journal-title":"J. Math. Phys."},{"key":"203_CR11","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.75.037201","volume":"75","author":"A. Iomin","year":"2007","unstructured":"Iomin, A.: Accelerator dynamics of a fractional kicked rotor. Phys. Rev. E 75, 037201 (2007), 4\u00a0pp.","journal-title":"Phys. Rev. E"},{"key":"203_CR12","doi-asserted-by":"crossref","first-page":"2984","DOI":"10.1016\/j.physleta.2008.01.037","volume":"372","author":"V.E. Tarasov","year":"2008","unstructured":"Tarasov, V.E.: Fractional Heisenberg equation. Phys. Lett. A 372, 2984\u20132988 (2008)","journal-title":"Phys. Lett. A"},{"key":"203_CR13","first-page":"463","volume":"21","author":"S.V. Ketov","year":"1990","unstructured":"Ketov, S.V., Prager Ya, S.: On the \u201csquare root\u201d of the Dirac equation within extended supersymmetry. Acta Phys. Pol. B 21, 463\u2013467 (1990)","journal-title":"Acta Phys. Pol. B"},{"key":"203_CR14","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1155\/S1110757X02110102","volume":"2","author":"P. Z\u00e1vada","year":"2002","unstructured":"Z\u00e1vada, P.: Relativistic wave equations with fractional derivatives and pseudodifferential operators. J.\u00a0Appl. Math. 2, 163\u2013197 (2002)","journal-title":"J.\u00a0Appl. Math."},{"key":"203_CR15","doi-asserted-by":"crossref","DOI":"10.1088\/1751-8113\/43\/5\/055203","volume":"43","author":"S.I. Muslih","year":"2010","unstructured":"Muslih, S.I., Agrawal, O.P., Baleanu, D.: A fractional Dirac equation and its solution. J. Phys. A 43, 055203 (2010), 13\u00a0pp.","journal-title":"J. Phys. A"},{"key":"203_CR16","doi-asserted-by":"crossref","first-page":"2756","DOI":"10.1016\/j.aop.2008.04.005","volume":"323","author":"V.E. Tarasov","year":"2008","unstructured":"Tarasov, V.E.: Fractional vector calculus and fractional Maxwell\u2019s equations. Ann. Phys. 323, 2756\u20132778 (2008)","journal-title":"Ann. Phys."},{"key":"203_CR17","doi-asserted-by":"crossref","first-page":"5515","DOI":"10.1016\/j.physleta.2008.06.063","volume":"372","author":"R. Herrmann","year":"2008","unstructured":"Herrmann, R.: Gauge invariance in fractional field theories. Phys. Lett. A 372, 5515\u20135522 (2008)","journal-title":"Phys. Lett. A"},{"key":"203_CR18","doi-asserted-by":"crossref","first-page":"3541","DOI":"10.1016\/j.physleta.2011.08.033","volume":"375","author":"M.J. Lazo","year":"2011","unstructured":"Lazo, M.J.: Gauge invariant fractional electromagnetic fields. Phys. Lett. A 375, 3541\u20133546 (2011)","journal-title":"Phys. Lett. A"},{"key":"203_CR19","unstructured":"Munkhammar, J.: Riemann\u2013Liouville fractional Einstein field equations (2010). arXiv:1003.4981 [physics.gen-ph]"},{"key":"203_CR20","doi-asserted-by":"crossref","first-page":"2888","DOI":"10.1016\/j.jnoncrysol.2005.05.035","volume":"351","author":"R.R. Nigmatullin","year":"2005","unstructured":"Nigmatullin, R.R., Le Mehaute, A.: Is there geometrical\/physical meaning of the fractional integral with complex exponent? J. Non-Cryst. Solids 351, 2888\u20132899 (2005)","journal-title":"J. Non-Cryst. Solids"},{"key":"203_CR21","first-page":"367","volume":"5","author":"I. Podlubny","year":"2002","unstructured":"Podlubny, I.: Geometric and physical interpretation of fractional integration and fractional differentiation. Fract. Calc. Appl. Anal. 5, 367\u2013386 (2002)","journal-title":"Fract. Calc. Appl. Anal."},{"key":"203_CR22","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1111\/j.1365-246X.1967.tb02303.x","volume":"13","author":"M. Caputo","year":"1967","unstructured":"Caputo, M.: Linear models of dissipation whose Q is almost frequency independent. Geophys. J. R. Astron. Soc. 13, 529\u2013539 (1967)","journal-title":"Geophys. J. R. Astron. Soc."},{"key":"203_CR23","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1007\/BF02820620","volume":"1","author":"M. Caputo","year":"1971","unstructured":"Caputo, M., Mainardi, F.: Linear models of dissipation in anelastic solids. Riv. Nuovo Cimento 1, 161\u2013198 (1971)","journal-title":"Riv. Nuovo Cimento"},{"key":"203_CR24","doi-asserted-by":"crossref","first-page":"1890","DOI":"10.1103\/PhysRevE.53.1890","volume":"53","author":"F. Riewe","year":"1996","unstructured":"Riewe, F.: Nonconservative Lagrangian and Hamiltonian mechanics. Phys. Rev. E 53, 1890\u20131899 (1996)","journal-title":"Phys. Rev. E"},{"key":"203_CR25","doi-asserted-by":"crossref","first-page":"3581","DOI":"10.1103\/PhysRevE.55.3581","volume":"55, part B","author":"F. Riewe","year":"1997","unstructured":"Riewe, F.: Mechanics with fractional derivatives. Phys. Rev. E 55, part B, 3581\u20133592 (1997)","journal-title":"Phys. Rev. E"},{"key":"203_CR26","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1073\/pnas.17.5.311","volume":"17","author":"P.S. Bauer","year":"1931","unstructured":"Bauer, P.S.: Dissipative dynamical systems: I. Proc. Natl. Acad. Sci. 17, 311\u2013314 (1931)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"203_CR27","doi-asserted-by":"crossref","first-page":"368","DOI":"10.1016\/S0022-247X(02)00180-4","volume":"272","author":"O.P. Agrawal","year":"2002","unstructured":"Agrawal, O.P.: Formulation of Euler\u2013Lagrange equations for fractional variational problems. J. Math. Anal. Appl. 272, 368\u2013379 (2002)","journal-title":"J. Math. Anal. Appl."},{"key":"203_CR28","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1007\/s10582-006-0406-x","volume":"56","author":"D. Baleanu","year":"2006","unstructured":"Baleanu, D., Agrawal, Om.P.: Fractional Hamilton formalism within Caputo\u2019s derivative. Czechoslov. J. Phys. 56, 1087\u20131092 (2006)","journal-title":"Czechoslov. J. Phys."},{"key":"203_CR29","volume":"48","author":"J. Cresson","year":"2007","unstructured":"Cresson, J.: Fractional embedding of differential operators and Lagrangian systems. J. Math. Phys. 48, 033504 (2007), 34\u00a0pp.","journal-title":"J. Math. Phys."},{"key":"203_CR30","doi-asserted-by":"crossref","first-page":"1009","DOI":"10.1016\/j.na.2011.02.028","volume":"75","author":"R. Almeida","year":"2012","unstructured":"Almeida, R., Pooseh, S., Torres, D.F.M.: Fractional variational problems depending on indefinite integrals. Nonlinear Anal. 75, 1009\u20131025 (2012)","journal-title":"Nonlinear Anal."},{"key":"203_CR31","doi-asserted-by":"crossref","first-page":"1490","DOI":"10.1016\/j.cnsns.2010.07.016","volume":"16","author":"R. Almeida","year":"2011","unstructured":"Almeida, R., Torres, D.F.M.: Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives. Commun. Nonlinear Sci. Numer. Simul. 16, 1490\u20131500 (2011)","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"203_CR32","doi-asserted-by":"crossref","first-page":"1507","DOI":"10.1016\/j.na.2011.01.010","volume":"75","author":"T. Odzijewicz","year":"2012","unstructured":"Odzijewicz, T., Malinowska, A.B., Torres, D.F.M.: Fractional variational calculus with classical and combined Caputo derivatives. Nonlinear Anal. 75, 1507\u20131515 (2012)","journal-title":"Nonlinear Anal."},{"key":"203_CR33","doi-asserted-by":"crossref","unstructured":"Odzijewicz, T., Malinowska, A.B., Torres, D.F.M.: Generalized fractional calculus with applications to the calculus of variations. Comput. Math. Appl. (2012, in press). doi: 10.1016\/j.camwa.2012.01.073","DOI":"10.1016\/j.camwa.2012.01.073"},{"key":"203_CR34","doi-asserted-by":"crossref","DOI":"10.1155\/2012\/871912","volume":"2012","author":"T. Odzijewicz","year":"2012","unstructured":"Odzijewicz, T., Malinowska, A.B., Torres, D.F.M.: Fractional calculus of variations in terms of a generalized fractional integral with applications to physics. Abstr. Appl. Anal. 2012, 871912 (2012), 24\u00a0pp.","journal-title":"Abstr. Appl. Anal."},{"key":"203_CR35","unstructured":"Cresson, J., Inizan, P.: Irreversibility, least action principle and causality (2009). arXiv:0812.3529 [math-ph]"},{"key":"203_CR36","doi-asserted-by":"crossref","first-page":"8297","DOI":"10.1088\/0305-4470\/36\/30\/307","volume":"36","author":"D.W. Dreisigmeyer","year":"2003","unstructured":"Dreisigmeyer, D.W., Young, P.M.: Nonconservative Lagrangian mechanics: a generalized function approach. J. Phys. A 36, 8297\u20138310 (2003)","journal-title":"J. Phys. A"},{"key":"203_CR37","doi-asserted-by":"crossref","DOI":"10.1142\/p871","volume-title":"Introduction to the Fractional Calculus of Variations","author":"A.B. Malinowska","year":"2012","unstructured":"Malinowska, A.B., Torres, D.F.M.: Introduction to the Fractional Calculus of Variations. Imperial College Press\/World Scientific, London\/Singapore (2012)"},{"key":"203_CR38","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/978-1-4614-0457-6_9","volume-title":"Fractional Dynamics and Control","author":"R. Almeida","year":"2012","unstructured":"Almeida, R., Malinowska, A.B., Torres, D.F.M.: Fractional Euler\u2013Lagrange differential equations via Caputo derivatives. In: Baleanu, D., Tenreiro Machado, J.A., Luo, A.C.J. (eds.) Fractional Dynamics and Control, pp. 109\u2013118. Springer, New York (2012)"},{"key":"203_CR39","volume-title":"Fractional Integrals and Derivatives","author":"S.G. Samko","year":"1993","unstructured":"Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives. Gordon and Breach, Yverdon (1993)"},{"key":"203_CR40","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-14574-2","volume-title":"The Analysis of Fractional Differential Equations","author":"K. Diethelm","year":"2010","unstructured":"Diethelm, K.: The Analysis of Fractional Differential Equations. Springer, Berlin (2010)"},{"key":"203_CR41","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1063\/1.166197","volume":"6","author":"K.M. Kolwankar","year":"1996","unstructured":"Kolwankar, K.M., Gangal, A.D.: Fractional differentiability of nowhere differentiable functions and dimensions. Chaos 6, 505\u2013513 (1996)","journal-title":"Chaos"},{"key":"203_CR42","first-page":"1949","volume":"2","author":"G. Jumarie","year":"2008","unstructured":"Jumarie, G.: From self-similarity to fractional derivative of non-differentiable functions via Mittag\u2013Leffler function. Appl. Math. Sci. 2, 1949\u20131962 (2008)","journal-title":"Appl. Math. Sci."},{"key":"203_CR43","volume-title":"Proceedings of the Fifth Symposium on Fractional Differentiation and Its Applications (FDA\u201912)","author":"X. Wang","year":"2012","unstructured":"Wang, X.: Fractional geometric calculus: toward a unified mathematical language for physics and engineering. In: Chen, W., Sun, H.-G., Baleanu, D. (eds.) Proceedings of the Fifth Symposium on Fractional Differentiation and Its Applications (FDA\u201912), Hohai University, Nanjing (2012). Paper #034"},{"key":"203_CR44","volume-title":"Calculus of Variations","author":"I.M. Gelfand","year":"1963","unstructured":"Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice Hall, Englewood Cliffs (1963)"}],"container-title":["Journal of Optimization Theory and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0203-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10957-012-0203-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10957-012-0203-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T09:55:19Z","timestamp":1559469319000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10957-012-0203-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,10,19]]},"references-count":44,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2013,1]]}},"alternative-id":["203"],"URL":"https:\/\/doi.org\/10.1007\/s10957-012-0203-6","relation":{},"ISSN":["0022-3239","1573-2878"],"issn-type":[{"value":"0022-3239","type":"print"},{"value":"1573-2878","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,10,19]]}}}