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

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  • Fathalla A. Rihan
  • Chinnathambi Rajivganthi
  • Palanisamy Muthukumar

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.

Suggested Citation

  • Fathalla A. Rihan & Chinnathambi Rajivganthi & Palanisamy Muthukumar, 2017. "Fractional Stochastic Differential Equations with Hilfer Fractional Derivative: Poisson Jumps and Optimal Control," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-11, June.
    • Handle: RePEc:hin:jnddns:5394528
    DOI: 10.1155/2017/5394528
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