Analytical investigation of fractional differential equations with combined nonlinearities and nonlocal closed fractional boundary conditions

This research presents an in-depth analysis of fractional differential equations characterized by combined nonlinearities and nonlocal closed boundary conditions of fractional order. The initial existence result is established employing the Leray–Schauder alternative, while the second existence result is derived through the application of Krasnoselskii’s theorem. Additionally, both the existence and uniqueness of solutions are established utilizing the Banach fixed-point theorem. The practical significance and applicability of the obtained results are demonstrated through an illustrative example in the concluding section. This study significantly contributes to advancing the understanding of intricate fractional differential equations and offers practical insights for a wide range of scientific and engineering applications.