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Existence and controllability of impulsive fractional stochastic differential equations driven by Rosenblatt process with Poisson jumps

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Abstract

The goal of this paper is to consider a new class of fractional stochastic differential equations driven by the Rosenblatt process with Poisson jumps and non-instantaneous impulses. By using fractional calculus, stochastic analysis, sectorial operator, and with the help of the fixed-point theorem, the existence of solutions is obtained for the proposed stochastic system. Moreover, we discuss the controllability of the proposed control system. Our main results are well supported by an illustrative example.

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Acknowledgements

We are very thankful to the anonymous reviewers and associate editor for their constructive comments and suggestions which helped us in improving the manuscript.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, India

    Rajesh Dhayal

  2. School of Basic Sciences, Indian Institute of Technology Mandi, Kamand, H.P., India

    Muslim Malik

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  1. Rajesh Dhayal
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  2. Muslim Malik
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Correspondence to Rajesh Dhayal.

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Dhayal, R., Malik, M. Existence and controllability of impulsive fractional stochastic differential equations driven by Rosenblatt process with Poisson jumps. J Eng Math 130, 11 (2021). https://doi.org/10.1007/s10665-021-10167-7

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  • DOI: https://doi.org/10.1007/s10665-021-10167-7

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