Approximate and trajectory controllability of fractional stochastic differential equation with non‐instantaneous impulses and Poisson jumps
Rajesh Dhayal, Muslim Malik, Syed Abbas
Abstract
Abstract The problem of approximate controllability is investigated in this paper for a class of fractional stochastic differential equations driven by fractional Brownian motion with non‐instantaneous impulses and Poisson jumps. The results are obtained by employing the η ‐resolvent family and Krasnoselskii's fixed point theorem. Further, we derive the trajectory controllability for the proposed stochastic control system. Finally, an example is provided to illustrate the obtained theory.
Topics & Concepts
ControllabilityMathematicsTrajectoryResolventStochastic differential equationFractional Brownian motionPoisson distributionMathematical analysisApplied mathematicsFixed-point theoremDifferential equationClass (philosophy)Brownian motionComputer sciencePhysicsAstronomyStatisticsArtificial intelligenceNonlinear Differential Equations AnalysisFractional Differential Equations SolutionsStability and Controllability of Differential Equations