An analysis of nonlinear integro-differential equations with four-point nonlocal BVP using Ψ-Caputo fractional derivative

This study establishes the existence and uniqueness of solutions for a nonlocal BVP of fractional order $1 < \zeta \leq 2$ , characterized by four-point boundary conditions and nonlinear integro-differential equations. The approach utilizes standard nonlinear theorems, which are instrumental in validating the existence of solutions across diverse mathematical and physical contexts. To illustrate the practical implications of the analytical results, a detailed example is presented, showcasing the applicability and effectiveness of the developed framework in solving complex boundary value problems.