Stability of a Nonlinear ML-Nonsingular Kernel Fractional Langevin System with Distributed Lags and Integral Control

The fractional Langevin equation has more advantages than its classical in representing the random motion of Brownian particles complex viscoelastic fluid. Mittag–Leffler (ML) without singularity is accurate and effective Riemann–Caputo (RC) Riemann–Liouville (RL) portraying motion. This paper focuses on a nonlinear ML-fractional system with distributed lag integral control. Employing fixed-point theorem generalised metric space established by Diaz Margolis, we built Hyers–Ulam–Rassias (HUR) stability along Hyers–Ulam (HU) this system. Applying our main results MATLAB software, have carried out theoretical analysis numerical simulation an example. By comparing corresponding system, it can be seen that better reflect stationarity statistical sense.