On the existence, uniqueness, and Ulam-Hyers stability of fractional Langevin equations with multi-point closed boundary conditions

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Abstract

This paper investigates the existence and uniqueness of mild solutions for a class of fractional Langevin equations subject to multi-point closed boundary conditions. By applying Krasnosel’skii fixed point theorem and the Banach contraction mapping principle, we establish sufficient conditions which ensure existence and uniqueness. Furthermore, we analyze the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the solutions within this framework. Illustrative examples are provided to demonstrate the applicability of the main results and to verify the stated hypotheses.

Keywords

fractional Langevin equation / multi-point closed boundary conditions / fixed point theorem / existence and uniqueness / Ulam-type stability

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