Fractional variational calculus for nondifferentiable functions

TL;DR

This paper develops necessary optimality conditions for variational problems involving nondifferentiable functions using Jumarie's modified Riemann-Liouville fractional derivative, extending classical calculus of variations to fractional, nondifferentiable contexts.

Contribution

It introduces necessary optimality conditions for fractional variational problems with nondifferentiable functions using Jumarie's derivative, including free boundary and constrained problems.

Findings

Derived necessary conditions for optimality in fractional variational problems.

Extended calculus of variations to nondifferentiable functions with fractional derivatives.

Addressed free boundary, isoperimetric, and holonomic constraints.

Abstract

We prove necessary optimality conditions, in the class of continuous functions, for variational problems defined with Jumarie's modified Riemann-Liouville derivative. The fractional basic problem of the calculus of variations with free boundary conditions is considered, as well as problems with isoperimetric and holonomic constraints.