Multiobjective fractional variational calculus in terms of a combined Caputo derivative

TL;DR

This paper develops necessary and sufficient optimality conditions for multiobjective fractional variational problems using a combined Caputo derivative, advancing the theoretical framework for fractional calculus in optimization.

Contribution

It introduces a new approach to fractional variational calculus with combined Caputo derivatives, including Euler-Lagrange, transversality, and Pareto optimality conditions.

Findings

Derived Euler-Lagrange equations for fractional variational problems.

Established transversality and sufficient optimality conditions.

Provided Pareto optimality conditions for multiobjective problems.

Abstract

The study of fractional variational problems in terms of a combined fractional Caputo derivative is introduced. Necessary optimality conditions of Euler-Lagrange type for the basic, isoperimetric, and Lagrange variational problems are proved, as well as transversality and sufficient optimality conditions. This allows to obtain necessary and sufficient Pareto optimality conditions for multiobjective fractional variational problems.