Journal of Applied Nonlinear Dynamics
Null Controllability of Nonlocal SobolevType Hilfer Fractional Stochastic Differential System Driven by Fractional Brownian Motion and Poisson Jumps
Journal of Applied Nonlinear Dynamics 10(4) (2021)
617626  DOI:10.5890/JAND.2021.12.003
K. Ravikumar , K. Ramkumar, A. Anguraj
Department of Mathematics, PSG College of Arts and Science, Coimbatore, 641 014, India
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Abstract
In this manuscript, we establish a class of nonlocal Sobolevtype Hilfer fractional stochastic differential equations driven by fractional Brownian motion, which is a special case of a selfsimilar process, Hermite processes with stationary increments with longrange dependence. The Hermite process of order 1 is fractional Brownian motion and of order 2 is the Rosenblatt process. By using fractional calculus and fixed point approach, sufficient conditions of exact null controllability for such fractional stochastic systems are established. The derived result in this manuscript is new in the sense that it generalizes many of the existing results in the literature, more precisely for fractional Brownian motion and Poisson jumps case of Sobolevtype Hilfer fractional stochastic settings. Finally, stochastic partial differential equations are provided to validate the applicability of the derived theoretical results.
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