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Research Article | Open Access

Study on a semilinear fractional stochastic system with multiple delays in control

Abdur Raheem1( ), Maryam G. Alshehri2( ), Asma Afreen1, Areefa Khatoon1, Musaad S. Aldhabani2
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia
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Abstract

This paper studies a semilinear fractional stochastic differential equation with multiple constant point delays in control. We transform the controllability problem into a fixed point problem. We obtain sufficient condition for the controllability by using Schauder's fixed point theorem. In addition, we discuss the optimal controllability of the problem. Some examples are given to illustrate the main result.

Keywords

Caputo fractional derivativecontrollabilitystochastic systemcontrolmultiple delays
CLC number: 34K35, 34K50, 93B05, 93E20

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AIMS Mathematics
Volume 7 Issue 7,
July 2022
Pages 12374-12389
DOI: 10.3934/math.2022687

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Cite this article:
Raheem A, Alshehri MG, Afreen A, et al. Study on a semilinear fractional stochastic system with multiple delays in control. AIMS Mathematics, 2022, 7(7): 12374-12389. https://doi.org/10.3934/math.2022687

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Received: 19 February 2022
Revised: 04 April 2022
Accepted: 12 April 2022
Published: 15 July 2022
©2022 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)