NUMERICAL SOLUTION FOR A NONLINEAR COUPLED SYSTEM OF LANGEVIN EQUATIONS VIA ABC FRACTIONAL OPERATORS

Abstract

The aims of this work is to investigate the behavior of a coupled system of Langevin equations with modified Atangana-Baleanu-Caputo (MABC) fractional derivatives,which has broad applicability in understanding and simulating physical and biological processescharacterized by random forces and uctuations. We seek to analyze the eect of the MABC fractional operator on the properties of the solution and develop the conditions for the existence and uniqueness of solutions by employing some fixed-point theorems. Additionally,we investigate Ulam stability to assess solution stability and sensitivity to perturbations.Furthermore, a numerical scheme is provided to showcase the obtained results, allowing forpractical simulations and a deeper understanding of the system's behavior. Overall, this study contributes valuable insights into the coupled Langevin equations with the modified Atangana-Baleanu-Caputo (MABC) fractional derivative, benefiting researchers in diversescientific fields.0