Fractional Calculus of Variations in Terms of a Generalized Fractional Integral with Applications to Physics

TL;DR

This paper develops a generalized fractional calculus of variations framework, deriving optimality conditions and boundary conditions, with applications to physics using the fractional action-like variational approach (FALVA).

Contribution

It introduces a new generalized fractional integral approach to variational problems, extending FALVA and applying it to physical models.

Findings

Derived necessary optimality conditions for fractional variational problems.

Extended FALVA to include generalized fractional integrals and derivatives.

Discussed applications of the framework to physics models.

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.