On multidimensional fractional Langevin equations  in terms of Caputo derivatives

Amele TAIEB 1 *, Sara BOUMESSAOUD 2 and Souad SALMI 3

doi:10.26637/MJM0804/0012

On multidimensional fractional Langevin equations in terms of Caputo derivatives

Authors :

Amele TAIEB ^{1 *}, Sara BOUMESSAOUD² and Souad SALMI ³

Author Address :

¹ LPAM, Faculty SEI, Mechanical Engineering Department, Faculty ST, UMAB Mostaganem, Algeria.
^2,3LPAM, Faculty SEI, UMAB Mostaganem, Algeria.

*Corresponding author.

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.

Keywords :

Caputo derivative, fixed point, fractional Langevin equation, existence and uniqueness, Ulam-Hyers stability.

DOI :

10.26637/MJM0804/0012

Article Info :

Received : April 04, 2020; Accepted : August 11, 2020.