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Research Article | Open Access

Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps

A. M. Sayed Ahmed1, Hamdy M. Ahmed2( ), Nesreen Sirelkhtam Elmki Abdalla3, Assmaa Abd-Elmonem3, E. M. Mohamed4
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt
Department of Mathematics, College of Science, Abha, King Khalid University, Saudi Arabia
Basic Science Department, Delta Higher Institute for Engineering and Technology, Egypt
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Abstract

In this paper, we explore the approximative controllability of fractional stochastic differential inclusions (SDIs) of Sobolev-type with fractional derivatives in Atangana-Baleanu (AB) sense and Poisson jumps. Our findings are supported by the fixed point theorem, multi-valued map theory, compact semigroup theory and stochastic analysis principles. In the later part, an illustration is provided to clarify the established outcomes.

Keywords

fractional calculusstochastic differential inclusionscontrol theoryPoisson jumps
CLC number: 34A08, 34A12, 34K37, 60H10, 93B05

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AIMS Mathematics
Volume 8 Issue 10,
October 2023
Pages 25288-25310
DOI: 10.3934/math.20231290

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Cite this article:
Sayed Ahmed AM, Ahmed HM, Abdalla NSE, et al. Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps. AIMS Mathematics, 2023, 8(10): 25288-25310. https://doi.org/10.3934/math.20231290

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Received: 30 May 2023
Revised: 31 July 2023
Accepted: 08 August 2023
Published: 15 October 2023
©2023 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)