Existence and uh-stability of integral boundary problem for a class of nonlinear higher-order Hadamard fractional Langevin equation via Mittag-Leffler functions

The Langevin equation is a very important mathematical model in describing the random motion of particles. fractional powerful tool complex viscoelasticity. Therefore, this paper focuses on class nonlinear higher-order Hadamard with integral boundary value conditions. Firstly, we employ successive approximation and Mittag-Leffler function to transform differential into an equivalent equation. Then existence uniqueness solution are obtained by using fixed point theory. Meanwhile, Ulam-Hyers (UH) stability proved inequality technique direct analysis.