Optimal Control Problems Involving Combined Fractional Operators with General Analytic Kernels

TL;DR

This paper introduces fractional optimal control problems with a broad class of operators having general analytic kernels, deriving necessary and sufficient optimality conditions, and providing an illustrative example.

Contribution

It develops a unified framework for fractional optimal control with general analytic kernels, including new optimality conditions and an example.

Findings

Derived Pontryagin-type necessary optimality conditions.

Proved a Mangasarian-type sufficient global optimality condition.

Presented an illustrative example demonstrating the theory.

Abstract

Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall type inequality as well as results on continuity and differentiability of perturbed trajectories. Moreover, a Mangasarian type sufficient global optimality condition for the general analytic kernel fractional optimal control problem is proved. An illustrative example is discussed.