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Research Article | Open Access

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

Abdelkader Moumen1, Ramsha Shafqat2( ), Ammar Alsinai3( ), Hamid Boulares4, Murat Cancan5, Mdi Begum Jeelani6
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
Department of mathematics, Kuvempu University, Shivamogga, Karnataka-577451, India
Laboratory of Analysis and Control of Differential Equations "ACED", Faculty MISM, Department of Mathematics, University 8 May 1945 Guelma, Algeria
Faculty of Education, Yuzuncu Yil University, Van 65080, Turkey
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh-13314, Saudi Arabia
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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.

Keywords

stochastic calculusHilfer derivativefinite approximate controllabilitysemi-groupfixed point theorystochastic evolution equations
CLC number: 34A07, 34A08, 60G22

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AIMS Mathematics
Volume 8 Issue 7,
July 2023
Pages 16094-16114
DOI: 10.3934/math.2023821

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Cite this article:
Moumen A, Shafqat R, Alsinai A, et al. Analysis of fractional stochastic evolution equations by using Hilfer derivative of finite approximate controllability. AIMS Mathematics, 2023, 8(7): 16094-16114. https://doi.org/10.3934/math.2023821

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Received: 21 January 2023
Revised: 23 April 2023
Accepted: 24 April 2023
Published: 15 July 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)