Investigation of optimal control results for generalized Riemann-Liouville fractional integrodifferential systems of Volterra-Fredholm type with nonlocal initial conditions

Abstract

This paper explores the optimal control results for generalized Riemann-Liouville (Hilfer) fractional Volterra-Fredholm integrodifferential systems of order eta is an element of(1,2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta \in (1,2)$$\end{document} under nonlocal conditions. First, the existence and uniqueness of mild solutions for the system are shown using the cosine family of operators and the Banach fixed point theorem. Then, the existence of an optimal control for the system is demonstrated. Finally, an example is provided to illustrate the obtained results.