Pontryagin maximum principle for fractional delay differential equations and controlled weakly singular Volterra delay integral equations

TL;DR

This paper applies the Pontryagin maximum principle to fractional delay differential equations and weakly singular Volterra delay integral equations, offering new methods for optimal control and illustrating results with examples.

Contribution

It extends the Pontryagin maximum principle to fractional delay and Volterra delay integral equations, providing a novel framework for optimal control in these contexts.

Findings

Derived optimal control conditions for fractional delay differential equations

Established the Pontryagin maximum principle for Volterra delay integral equations

Provided illustrative examples demonstrating the theoretical results

Abstract

In this article, we explore two distinct issues. Initially, we examine the utilization of the Pontriagin maximum principle in relation to fractional delay differential equations. Additionally, we discuss the optimal approach for solving the control problem for equation (1.1) and its associated payoff function (1.2). Following that, we investigate the application of the Pontryagin Maximum principle in the context of Volterra delay integral equations (1.3). We strengthen the results of our study by providing illustrative examples at the end of the article.