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

Abdur Raheem; Maryam G. Alshehri; Asma Afreen; Areefa Khatoon; Musaad S. Aldhabani; Abdur Raheem; Maryam G. Alshehri; Asma Afreen; Areefa Khatoon; Musaad S. Aldhabani

doi:10.3934/math.2022687

AIMS Mathematics

2022, Volume 7, Issue 7: 12374-12389. doi: 10.3934/math.2022687

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Research article

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

1.
Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India
2.
Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Received: 19 February 2022 Revised: 04 April 2022 Accepted: 12 April 2022 Published: 25 April 2022
MSC : 34K35, 34K50, 93B05, 93E20

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.
- Caputo fractional derivative,
- controllability,
- stochastic system,
- control,
- multiple delays
Citation: Abdur Raheem, Maryam G. Alshehri, Asma Afreen, Areefa Khatoon, Musaad S. Aldhabani. Study on a semilinear fractional stochastic system with multiple delays in control[J]. AIMS Mathematics, 2022, 7(7): 12374-12389. doi: 10.3934/math.2022687

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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.

References

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