Applications of the Mittag-Leffler function in solvability and stability of a class of fractional Langevin equations with two fractional orders

This study focuses on the solvability and Hyers-Ulam stability of a particular class of fractional Langevin equations with two fractional orders. Utilizing the Mittag-Leffler functions, we present a representation of the general solution for the problem. Our approach offers significant technical advantages compared to existing literature. Furthermore, we furnish illustrative examples, employing specific parameters, to showcase the existence of a unique solution and its Hyers-Ulam stability even under less restrictive conditions.