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

Mohamed Adel; M. Elsaid Ramadan; Hijaz Ahmad; Thongchai Botmart; Mohamed Adel; M. Elsaid Ramadan; Hijaz Ahmad; Thongchai Botmart

doi:10.3934/math.20221100

AIMS Mathematics

2022, Volume 7, Issue 11: 20105-20125. doi: 10.3934/math.20221100

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Research article

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

1.
Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
2.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina, Saudi Arabia
3.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

Received: 27 March 2022 Revised: 28 May 2022 Accepted: 18 July 2022 Published: 13 September 2022
MSC : 26A33, 34A37, 34K37, 93B05

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.
Citation: Mohamed Adel, M. Elsaid Ramadan, Hijaz Ahmad, Thongchai Botmart. Sobolev-type nonlinear Hilfer fractional stochastic differential equations with noninstantaneous impulsive[J]. AIMS Mathematics, 2022, 7(11): 20105-20125. doi: 10.3934/math.20221100

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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.

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