Solvability and stability of a class of fractional Langevin differential equations with the Mittag–Leffler function

In the present paper, the solvability and stability of a class of fractional Langevin equations with integral and anti-periodic boundary conditions are considered. By applying the Krasnoselskii fixed point theorem, the Banach contraction mapping theorem, and specific properties of the Mittag–Leffler function, we derive weaker sufficient conditions for the existence, uniqueness, and stability of results, building upon prior work in this literature. Some illustrative numerical examples are also discussed to demonstrate the superiority of our results.