Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics
arXiv:1203.1961 · doi:10.1155/2012/871912
Abstract
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to Physics discussed.
arXiv commentSubmitted 01/Jan/2012; revised 25/Feb/2012; accepted 27/Feb/2012; for publication in Abstract and Applied Analysis (http://www.hindawi.com/journals/aaa/)
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Cited by in corpus (12)
- Hermite-Hadamard and Hermite-Hadamard-Fejér type Inequalities for Generalized Fractional Integrals
- Discrete Direct Methods in the Fractional Calculus of Variations
- Fractional variational calculus of variable order
- Mellin Transforms of the Generalized Fractional Integrals and Derivatives
- Fractional Herglotz Variational Principles with Generalized Caputo Derivatives
- Green's Theorem for Generalized Fractional Derivatives
- The DuBois-Reymond Fundamental Lemma of the Fractional Calculus of Variations and an Euler-Lagrange Equation Involving only Derivatives of Caputo
- Generalized Transversality Conditions in Fractional Calculus of Variations
- Fractional Calculus of Variations of Several Independent Variables
- Variable Order Fractional Variational Calculus for Double Integrals
- Generalized fractional operators for nonstandard Lagrangians
- Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives