Generalizations of Darbo’s fixed point-theorem and its application to the solvability of a nonlinear fractional differential equation

Abstract

This paper introduces novel fixed-point theorems for generalized Proinov contraction mappings utilizing the measure of noncompactness. These results significantly extend existing contraction principles and provide novel methods for analyzing nonlinear problems. We demonstrate the practical power of our theorems by establishing the existence of solutions to a broad class of nonlinear fractional differential equations with integral boundary conditions. An illustrative example underscores the effectiveness of our approach, promising impactful applications in fractional calculus and nonlinear analysis. Overall, these results enrich the theoretical framework and offer valuable insights for researchers working on complex dynamical systems and applied mathematical models.