Null Controllability of Nonlocal Hilfer Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Poisson Jumps

EasyChair Preprint 5735

Abstract

This manuscript investigates a class of nonlocal Hilfer fractional stochastic differential equations driven by fractional Brownian motion, which is a special case of a self-similar process, Hermite processes with stationary increments with long-range dependence. The Hermite process of order 1 is fractional Brownian motion and of order 2 is the Rosenblatt process. We establish new sufficient conditions of exact null controllability for such stochastic settings by using fractional calculus and fixed point theorem. The derived result in this article 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 Hilfer fractional stochastic settings.

Keyphrases: Hilfer fractional derivative, Null controllability., Poisson jumps, Rosenblatt process, Stochastic differential, fractional Brownian motion, stochastic differential equation

@booklet{EasyChair:5735,
  author    = {Dimplekumar Chalishajar and K Ramkumar and K Ravikumar and A Anguraj},
  title     = {Null Controllability of Nonlocal Hilfer Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Poisson Jumps},
  howpublished = {EasyChair Preprint 5735},
  year      = {EasyChair, 2021}}