Approximate controllability of Atangana- Baleanu fractional stochastic differential systems with non-Gaussian process and impulses
Rajesh Dhayal, Yuxiao Zhao, Quanxin Zhu, Zengyun Wang, Mohammad Bagher Karimi
Abstract
This paper aims to investigate a new class of Atangana-Baleanu fractional stochastic differential systems under the influence of the Rosenblatt process and non-instantaneous impulses. We analyze the existence and uniqueness of piecewise continuous mild solutions by using the fixed point method, fractional calculus, and resolvent family. Further, we define a new piecewise control function and investigate the approximate controllability results for the proposed problem. Finally, the main results are validated with the aid of an example.
Topics & Concepts
ControllabilityMathematicsProcess (computing)Stochastic differential equationGaussian processApplied mathematicsGaussianStochastic processDifferential (mechanical device)Ornstein–Uhlenbeck processMathematical analysisStatistical physicsComputer sciencePhysicsStatisticsQuantum mechanicsThermodynamicsOperating systemNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations