Existence of Solutions for a Coupled System of Ψ-Caputo Fractional Differential Equations With Integral Boundary Conditions

In this study, we examine a system of fractional differential equations involving nonlinear terms that depend on unknown functions and their fractional derivatives. We propose coupled nonlocal boundary conditions with integral constraints, introducing a novel problem within fractional calculus and nonlinear dynamics. Our main contributions include proving the existence of solutions obtained via Leray-Schauder's alternative and establishing uniqueness via the contraction mapping principle. These findings are further supported by examples that showcase the system's mathematical properties and behavior.