Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability

Abdelkader Moumen; Ramsha Shafqat; Ammar Alsinai; Hamid Boulares; Murat Cancan; Mdi Begum Jeelani; Abdelkader Moumen; Ramsha Shafqat; Ammar Alsinai; Hamid Boulares; Murat Cancan; Mdi Begum Jeelani

doi:10.3934/math.2023821

AIMS Mathematics

2023, Volume 8, Issue 7: 16094-16114. doi: 10.3934/math.2023821

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Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability

1.
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
2.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
3.
Department of mathematics, Kuvempu University, Shivamogga, Karnataka-577451, India
4.
Laboratory of Analysis and Control of Differential Equations "ACED", Faculty MISM, Department of Mathematics, University 8 May 1945 Guelma, Algeria
5.
Faculty of Education, Yuzuncu Yil University, Van 65080, Turkey
6.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh-13314, Saudi Arabia

Received: 21 January 2023 Revised: 23 April 2023 Accepted: 24 April 2023 Published: 05 May 2023
MSC : 34A07, 34A08, 60G22

The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstrated using an example. A conclusion is given at the end.
- stochastic calculus,
- Hilfer derivative,
- finite approximate controllability,
- semi-group,
- fixed point theory,
- stochastic evolution equations
Citation: Abdelkader Moumen, Ramsha Shafqat, Ammar Alsinai, Hamid Boulares, Murat Cancan, Mdi Begum Jeelani. Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability[J]. AIMS Mathematics, 2023, 8(7): 16094-16114. doi: 10.3934/math.2023821

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Abstract

The approximate controllability of a class of fractional stochastic evolution equations (FSEEs) are discussed in this study utilizes the Hilbert space by using Hilfer derivative. For different approaches, we remove the Lipschitz or compactness conditions and merely have to assume a weak growth requirement. The fixed point theorem, the diagonal argument, and approximation methods serve as the foundation for the study. The abstract theory is demonstrated using an example. A conclusion is given at the end.

References

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