Solvability of Infinite Systems of Nonlinear Caputo Fractional Differential equations in generalized Hahn Sequence Space

Abstract

This paper presents the Hausdorff measure of noncompactness (MNC) within the framework of the generalized Hahn sequence space. By applying the MNC, we explore the existence of solutions for nonlinear Caputo fractional differential equations subject to three-point integral boundary conditions in the generalized Hahn sequence space. We apply certain sufficient conditions to ensure the uniqueness of solutions to the aforementioned problem, utilizing the Banach fixed-point theorem, and discuss the Hyers-Ulam stability of the problem. In conclusion, the analytical framework is complemented by illustrative examples that demonstrate the validity and applicability of the main results.