Existence and Hyers-Ulam stability of a coupled fractional differential system involving the \({\rm{\Psi\ }}\)-Caputo derivative and mixed boundary conditions

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 \(\Psi\)-Riemann-Liouville fractional integral evaluated at the interior point \(\gamma\). Furthermore, the Hyers-Ulam stability of the proposed system is examined. Finally, an illustrative example is provided to support the theoretical findings.