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Fractional variational calculus with classical and combined Caputo derivatives

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Feb 2012Embargo end date: 01 Jan 2011 Portugal Publisher:Elsevier BVJournal:Nonlinear Analysis: Theory, Methods & Applications, volume 75, pages 1,507-1,515 (issn: 0362-546X, Copyright policy )
Authors: Odzijewicz, T.; Malinowska, A. B.; Torres, D. F. M.;

doi: 10.1016/j.na.2011.01.010 , 10.48550/arxiv.1101.2932

arXiv: http://arxiv.org/abs/1101.2932

handle: 10773/11903

Fractional variational calculus with classical and combined Caputo derivatives

Abstract

We give a proper fractional extension of the classical calculus of variations by considering variational functionals with a Lagrangian depending on a combined Caputo fractional derivative and the classical derivative. Euler-Lagrange equations to the basic and isoperimetric problems are proved, as well as transversality conditions.

Submitted 30-Nov-2010; accepted 14-Jan-2011; for publication in Nonlinear Analysis Series A: Theory, Methods & Applications

Country
Portugal
Related Organizations
Keywords

Differentiation (calculus), 49K05, 49K21, 26A33, 34A08, Fractional derivatives, Fractional variational analysis, Natural boundary conditions, Optimization and Control (math.OC), FOS: Mathematics, Euler-Lagrange equations, Variational analysis, Calculations, Isoperimetric problems, Mathematics - Optimization and Control, Variational techniques

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
101
Top 10%
Top 10%
Top 1%
Green
bronze