Existence and Hyers-Ulam stability of a coupled fractional differential system involving the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-6

Abstract

In this study, the Banach contraction principle and Schaefer’s fixed point theorem are employed to establish, respectively, the uniqueness and existence of solutions for a coupled fractional differential system subject to mixed boundary conditions. These conditions consist of Dirichlet conditions and nonlocal fractional integral conditions involving the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Psi$$\end{document}-Riemann-Liouville fractional integral evaluated at the interior point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma$$\end{document}. Furthermore, the Hyers-Ulam stability of the proposed system is examined. Finally, an illustrative example is provided to support the theoretical findings.