Variational Problems Involving a Caputo-Type Fractional Derivative

Ricardo Almeida

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arXiv · 1601.07376

Variational Problems Involving a Caputo-Type Fractional Derivative

Ricardo Almeida

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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.

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Ricardo Almeida. 2016-01-24. Variational Problems Involving a Caputo-Type Fractional Derivative. https://arxiv.org/abs/1601.07376

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