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Research Article | Open Access

Sobolev-type nonlinear Hilfer fractional stochastic differential equations with noninstantaneous impulsive

Mohamed Adel1, M. Elsaid Ramadan2, Hijaz Ahmad3, Thongchai Botmart4( )
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand
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An erratum to this article is available online at:
https://doi.org/10.3934/math.2023460

Abstract

The existence of a mild solution for nonlinear Hilfer fractional stochastic differential equations of the Sobolev type with non-instantaneous impulse in Hilbert space is investigated in this study. For nonlinear Hilfer fractional stochastic differential equations of Sobolev type with non-instantaneous impulsive conditions, sufficient criteria for controllability are established. Finally, an illustration of the acquired results is shown.

Keywords

Sobolev-type nonlinear Hilfer fractional stochastic differential equationexistence solutionscontrollabilitynoninstantaneous impulsive condition
CLC number: 26A33, 34A37, 34K37, 93B05

References

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AIMS Mathematics
Volume 7 Issue 11,
November 2022
Pages 20105-20125
DOI: 10.3934/math.20221100

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Cite this article:
Adel M, Ramadan ME, Ahmad H, et al. Sobolev-type nonlinear Hilfer fractional stochastic differential equations with noninstantaneous impulsive. AIMS Mathematics, 2022, 7(11): 20105-20125. https://doi.org/10.3934/math.20221100

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Received: 27 March 2022
Revised: 28 May 2022
Accepted: 18 July 2022
Published: 15 November 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)