Isoperimetric problems of the calculus of variations with fractional derivatives

TL;DR

This paper investigates isoperimetric problems within the calculus of variations involving fractional derivatives, analyzing cases where the bounds of the integrals and derivatives align or differ, advancing understanding of fractional variational problems.

Contribution

It introduces a comprehensive study of isoperimetric problems with Riemann-Liouville fractional derivatives considering different boundary conditions.

Findings

Derived necessary optimality conditions for fractional isoperimetric problems.

Analyzed cases with coinciding and non-coinciding bounds of integrals and derivatives.

Extended classical calculus of variations to fractional derivatives with new theoretical results.

Abstract

In this paper we study isoperimetric problems of the calculus of variations with left and right Riemann-Liouville fractional derivatives. Both situations when the lower bound of the variational integrals coincide and do not coincide with the lower bound of the fractional derivatives are considered.