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Exact Null Controllability of Sobolev-Type Hilfer Fractional Stochastic Differential Equations with Fractional Brownian Motion and Poisson Jumps

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Abstract

In this paper, we establish sufficient conditions for exact null controllability of Sobolev type stochastic differential equations with fractional Brownian motion and Poisson jumps in Hilbert spaces, where the time fractional derivative is the Hilfer derivative. The exact null controllability result is derived by using fractional calculus, compact semigroup, fixed point theorem and stochastic analysis. Finally, an example is given to show the application of our results.

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Authors and Affiliations

  1. Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt

    Hamdy M. Ahmed

  2. Department of Mathematics, Guizhou University, Guiyang, 55002, Guizhou, China

    JinRong Wang

  3. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, Shandong, China

    JinRong Wang

Authors
  1. Hamdy M. Ahmed
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  2. JinRong Wang
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Correspondence to JinRong Wang.

Additional information

This work is supported by Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006) and Science and Technology Program of Guizhou Province ([2017]5788).

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Ahmed, H.M., Wang, J. Exact Null Controllability of Sobolev-Type Hilfer Fractional Stochastic Differential Equations with Fractional Brownian Motion and Poisson Jumps. Bull. Iran. Math. Soc. 44, 673–690 (2018). https://doi.org/10.1007/s41980-018-0043-8

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  • DOI: https://doi.org/10.1007/s41980-018-0043-8

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