Fractional variational calculus for non-differentiable functions, chapter

TL;DR

This paper develops a fractional calculus of variations framework using Jumarie's fractional derivatives, enabling analysis of non-differentiable functions and deriving optimality conditions for variational problems.

Contribution

It introduces a new approach to fractional variational calculus based on Jumarie's derivatives, extending the applicability to non-differentiable functions.

Findings

Derived necessary optimality conditions for fractional variational problems.

Established sufficient conditions for optimality.

Extended calculus of variations to non-differentiable functions using fractional operators.

Abstract

The fractional calculus of variations is now a subject under strong research. Different definitions for fractional derivatives and integrals are used, depending on the purpose under study. In this paper the fractional operators are defined in the sense of Jumarie. This allows us to work with functions which are non-differentiable. We present necessary and sufficient optimality conditions for fractional problems of the calculus of variations with a Lagrangian density depending on the free end-points.