Stability of nonlocal fractional Langevin differential equations involving fractional integrals

In this paper, we investigate Ulam-Hyers stability, Practical-Ulam-Hyers stability and Practical-Ulam-Hyers-Rassias stability of nonlocal fractional Langevin equations involving Riemann-Liouville fractional integral with positive constant coefficients. By utilizing an explicit bound of Mittag-Leffler function with two parameters and analytical methods, the practical stability results are presented via a generalized Gronwall inequality. Finally, two examples are given to illustrate our theoretical results.