Stability of a Nonlinear Langevin System of ML-Type Fractional Derivative Affected by Time-Varying Delays and Differential Feedback Control

The Langevin system is an important mathematical model to describe Brownian motion. research shows that fractional differential equations have more advantages in viscoelasticity. exploration of dynamics novel and valuable. Compared with the Caputo or Riemann–Liouville (RL) derivatives, Mittag–Leffler (ML)-type derivatives can eliminate singularity such solution has better analytical properties. Therefore, we concentrate on a nonlinear ML-type affected by time-varying delays feedback control manuscript. We first utilize two fixed-point theorems proposed Krasnoselskii Schauder investigate existence solution. Next, employ contraction mapping principle analysis establish stability types as Ulam–Hyers (UH) Ulam–Hyers–Rassias (UHR) well generalized UH UHR. Lastly, theoretical numerical simulation some interesting examples are carried out using our main results DDESD toolbox MATLAB.