Variational Problems Involving a Caputo-Type Fractional Derivative
arXiv:1601.07376
Abstract
The aim of this paper is to study certain problems of calculus of variations, that are dependent upon a Lagrange function on a Caputo-type fractional derivative. This type of fractional operator is a generalization of the Caputo and the Caputo--Hadamard fractional derivatives, that are dependent on a real parameter ro. Sufficient and necessary conditions of the first and second order are presented. The cases of integral and holonomic constraints are also considered.
This is a preprint of a paper whose final and definite form will be published in Journal of Optimization Theory and Applications
References in corpus (4)
- Calculus of variations with fractional derivatives and fractional integrals
- Fractional Noether's theorem in the Riesz-Caputo sense
- The generalized natural boundary conditions for fractional variational problems in terms of the Caputo derivative
- The Legendre Condition of the Fractional Calculus of Variations