Statistics

Machine learning

Mathematical analysis

Langevin equation

Artificial intelligence

Brownian motion

Stability (learning theory)

Physics

Exponential function

Nonlinear system

Uniqueness

Kernel (algebra)

Pure mathematics

Langevin dynamics

Mathematics

Quantum mechanics

Fractional Brownian motion

Computer science

Statistical physics

Control (management)

Invertible matrix

Applied mathematics

Control theory (sociology)

Discrete Dynamics in Nature and Society

Fractional Langevin system has great advantages in describing the random motion of Brownian particles in complex viscous fluid. This manuscript deals with a delayed nonlinear fractional Langevin system with nonsingular exponential kernel. Based on the fixed point theory, some sufficient criteria for the existence and uniqueness of solution are established. We also prove that this system is UH‐ and UHR‐stable attributed to the nonlinear analysis and inequality techniques. As applications, we provide some examples and simulations to illustrate the availability of main findings.

Stability of a Nonlinear Fractional Langevin System with Nonsingular Exponential Kernel and Delay Control