Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order

TL;DR

This paper derives necessary optimality conditions for fractional variational problems involving a combined Caputo derivative of variable order, including transversality conditions for free endpoints, with illustrative particular cases.

Contribution

It introduces new optimality conditions for variational problems with a combined Caputo derivative of variable order, expanding fractional calculus applications.

Findings

Established necessary optimality conditions for the problems.

Derived transversality conditions for free endpoints.

Presented illustrative particular cases.

Abstract

We establish necessary optimality conditions for variational problems with a Lagrangian depending on a combined Caputo derivative of variable fractional order. The endpoint of the integral is free, and thus transversality conditions are proved. Several particular cases are considered illustrating the new results.