Composition Functionals in Fractional Calculus of Variations

TL;DR

This paper develops necessary optimality conditions for fractional calculus of variations problems involving compositions of functionals, using Riemann-Liouville derivatives and integrals in the sense of Jumarie, with applications to products and quotients.

Contribution

It introduces new Euler-Lagrange and boundary conditions for fractional variational problems with composed functionals, expanding the theoretical framework.

Findings

Derived Euler-Lagrange equations for composed fractional functionals

Established natural boundary conditions in the fractional setting

Applied results to product and quotient of fractional functionals

Abstract

We prove Euler-Lagrange and natural boundary necessary optimality conditions for fractional problems of the calculus of variations which are given by a composition of functionals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. As an application, we get optimality conditions for the product and the quotient of fractional variational functionals.