Study of a Coupled Ψ–Liouville–Riemann Fractional Differential System Characterized by Mixed Boundary Conditions

This research is concerned with the existence and uniqueness of solutions for a coupled system of Ψ–Riemann–Liouville fractional differential equations. To achieve this objective, we establish a set of necessary conditions by formulating the problem as an integral equation and utilizing well-known fixed-point theorems. By employing these mathematical tools, we demonstrate the existence and uniqueness of solutions for the proposed system. Additionally, to illustrate the practical implications of our findings, we provide several examples that showcase the main results obtained in this study.