Analysis of a nonlinear Caputo fractional coupled system with integral boundary conditions in Banach spaces

Abstract

In this work, we investigate a nonlinear coupled system of Caputo fractional differential equations subject to integral boundary conditions in the framework of Banach spaces. The analysis is conducted through a fixed point approach. First, the existence of mild solutions is established by employing the Kuratowski measure of noncompactness together with the Generalized Darbo's theorem involving a nondecreasing control function. Uniqueness of the solution is then obtained using the Banach contraction principle. In addition, we study the continuous dependence of the solutions on the input functions, which ensures the stability of the model under perturbations. The Ulam--Hyers stability of the system is also investigated, ensuring that small perturbations in the initial functions lead to proportionally small changes in the solution. These results contribute to the well-posedness and robustness of the proposed fractional model. Finally, a concrete example is provided to illustrate the applicability and effectiveness of the theoretical results obtained.