Stability of a Nonlinear Fractional Langevin System with Nonsingular Exponential Kernel and Delay Control
Kaihong Zhao
Abstract
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.
Topics & Concepts
Invertible matrixNonlinear systemUniquenessMathematicsKernel (algebra)Brownian motionApplied mathematicsExponential functionLangevin dynamicsStability (learning theory)Langevin equationFractional Brownian motionStatistical physicsControl theory (sociology)Mathematical analysisPhysicsComputer scienceControl (management)Pure mathematicsStatisticsArtificial intelligenceMachine learningQuantum mechanicsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisStability and Controllability of Differential Equations