On the Existence of Solutions for a Fractional Differential Boundary Value Problem via DarboType Fixed Point

Abstract

In this work, we study the existence of solutions for a class of fractional boundary value problems involving the Caputo fractional derivative. Our approach is based on transforming the considered boundary value problems into an equivalent fixed-point equation by applying fixed-point results related to generalized Proinov-type contraction mappings defined through the measure of noncompactness. The obtained results substantially extend classical contraction principles and offer powerful tools for the analysis of nonlinear problems. An illustrative example is presented to demonstrate the significance and the applicability of the obtained results.