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

A. M. Sayed Ahmed; Hamdy M. Ahmed; Nesreen Sirelkhtam Elmki Abdalla; Assmaa Abd-Elmonem; E. M. Mohamed; A. M. Sayed Ahmed; Hamdy M. Ahmed; Nesreen Sirelkhtam Elmki Abdalla; Assmaa Abd-Elmonem; E. M. Mohamed

doi:10.3934/math.20231290

AIMS Mathematics

2023, Volume 8, Issue 10: 25288-25310. doi: 10.3934/math.20231290

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Research article

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

1.
Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
2.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El-Shorouk Academy, El-Shorouk City, Cairo, Egypt
3.
Department of Mathematics, College of Science, Abha, King Khalid University, Saudi Arabia
4.
Basic Science Department, Delta Higher Institute for Engineering and Technology, Egypt

Received: 30 May 2023 Revised: 31 July 2023 Accepted: 08 August 2023 Published: 30 August 2023
MSC : 34A08, 34A12, 34K37, 60H10, 93B05

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.
- fractional calculus,
- stochastic differential inclusions,
- control theory,
- Poisson jumps
Citation: A. M. Sayed Ahmed, Hamdy M. Ahmed, Nesreen Sirelkhtam Elmki Abdalla, Assmaa Abd-Elmonem, E. M. Mohamed. Approximate controllability of Sobolev-type Atangana-Baleanu fractional differential inclusions with noise effect and Poisson jumps[J]. AIMS Mathematics, 2023, 8(10): 25288-25310. doi: 10.3934/math.20231290

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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.

References

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