On multidimensional fractional Langevin equations in terms of Caputo derivatives

Abstract

In this paper, we consider a more general and multidimensional fractional Langevin equations with nonlinear terms that involve some unknown functions and their Caputo derivatives. Using some fixed point theorems, we obtain new results on the existence and uniqueness of solutions in addition to the existence of at least one solution. We also define and prove the generalized Ulam-Heyers stability of solutions for the considered equations. Some examples are provided to illustrate the applications of our results.