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Approximate Controllability for Hilfer Fractional Stochastic Non-instantaneous Impulsive Differential System with Rosenblatt Process and Poisson Jumps

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Abstract

This paper discusses the approximate controllability of Hilfer fractional stochastic differential system involving non-instantaneous impulses with Rosenblatt process and Poisson jumps. By utilising stochastic analysis, semigroup theory, fractional calculus, and Krasnoselskii’s fixed point theorem, we prove our primary outcomes. Firstly, we prove the approximate controllability of the Hilfer fractional system. As a final step, we provide an example to highlight our discussion.

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Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

Abbreviations

FDEs:

Fractional differential equations

HFSNIIDS:

Hilfer fractional stochastic non-instantaneous impulsive differential system

R–L:

Riemann–Liouville

HF:

Hilfer fractional

HFD:

Hilfer fractional derivative

SDEs:

Stochastic differential equations

fBm:

Fractional Brownian motion

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Acknowledgements

The authors also would like to thank the reviewer and the editor for their valuable comments and suggestions which improved the quality of the paper.

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Authors and Affiliations

  1. Department of Mathematics School of Advanced Sciences, Vellore Institute of Technology, Vellore, 632 014, Tamil Nadu, India

    G. Gokul & R. Udhayakumar

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  1. G. Gokul
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Contributions

Conceptualisation, G.Gokul(G.G) and R.Udhayakumar (R.U.); methodology, G.G.; validation, G.G. and R.U.; formal analysis, G.G.; investigation, R.U.; resources, G.G.; writing original draft preparation, G.G.; writing review and editing, R.U.; visualisation, R.U.; supervision, R.U.; project administration, R.U. All authors have read and agreed to the published version of the paper. All the authors are equally contributed to this paper.

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Correspondence to R. Udhayakumar.

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Gokul, G., Udhayakumar, R. Approximate Controllability for Hilfer Fractional Stochastic Non-instantaneous Impulsive Differential System with Rosenblatt Process and Poisson Jumps. Qual. Theory Dyn. Syst. 23, 56 (2024). https://doi.org/10.1007/s12346-023-00912-x

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