Fractional Variational Calculus with Classical and Combined Caputo Derivatives
By Tatiana Odzijewicz, Agnieszka B. Malinowska, Delfim F. M. Torres. 2011
129 citations recorded by the source corpus.
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 as well as transversality conditions are proved.
Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/fcaefd8cef5a22b7d6104248e8ce5e816fbb2968
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In Applied Mathematics
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Pontryagin maximum principle for general Caputo fractional optimal control problems with Bolza cost and terminal constraints (2020, unknown): “We refer for example to [2, 6, 7, 9, 12, 21, 41, 43, 57] and references therein.”
- Numerical solution of fractional Sturm-Liouville equation in integral form (2014, unknown): “Other applications of fractional variational principles are presented in [2, 19, 25, 26, 28].”
- Existence of a weak solution for fractional Euler-Lagrange equations (2012, background): “Furthermore, one can find a comprehensive literature regarding necessary optimality conditions and Noether’s theorem, see [1, 3, 4, 6, 13, 25].”