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

ABSTRACT 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.