Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control

Author:

Rihan Fathalla A.1ORCID,Rajivganthi Chinnathambi1,Muthukumar Palanisamy2

Affiliation:

1. Department of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAE

2. Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, India

Abstract

In this work, we consider a class of fractional stochastic differential system with Hilfer fractional derivative and Poisson jumps in Hilbert space. We study the existence and uniqueness of mild solutions of such a class of fractional stochastic system, using successive approximation theory, stochastic analysis techniques, and fractional calculus. Further, we study the existence of optimal control pairs for the system, using general mild conditions of cost functional. Finally, we provide an example to illustrate the obtained results.

Funder

UAE University

Publisher

Hindawi Limited

Subject

Modelling and Simulation

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