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Discrete Dynamics in Nature and Society
Volume 2017 (2017), Article ID 5394528, 11 pages
Research Article

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

1Department of Mathematical Sciences, College of Science, UAE University, Al-Ain 15551, UAE
2Department of Mathematics, Gandhigram Rural Institute-Deemed University, Gandhigram, Tamil Nadu 624 302, India

Correspondence should be addressed to Fathalla A. Rihan

Received 18 January 2017; Revised 20 April 2017; Accepted 4 May 2017; Published 15 June 2017

Academic Editor: Thabet Abdeljawad

Copyright © 2017 Fathalla A. Rihan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.