Controllability of fractional stochastic evolution inclusion via Hilfer derivative of fixed point theory

Abdelkader Moumen; Ammar Alsinai; Ramsha Shafqat; Nafisa A. Albasheir; Mohammed Alhagyan; Ameni Gargouri; Mohammed M. A. Almazah; Abdelkader Moumen; Ammar Alsinai; Ramsha Shafqat; Nafisa A. Albasheir; Mohammed Alhagyan; Ameni Gargouri; Mohammed M. A. Almazah

doi:10.3934/math.20231014

AIMS Mathematics

2023, Volume 8, Issue 9: 19892-19912. doi: 10.3934/math.20231014

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Controllability of fractional stochastic evolution inclusion via Hilfer derivative of fixed point theory

1.
Department of Mathematics, Faculty of Sciences, University of Hail, Hail 55425, Saudi Arabia
2.
Department of mathematics, Kuvempu University, Shivamogga, Karnataka-577451, India
3.
Department of Mathematics and Statistics, The University of Lahore, Sargodha 40100, Pakistan
4.
Department of Mathematics, College of Science and Arts (Magardah), King Khalied University, Magardah 61421, Saudi Arabia
5.
Department of Mathematics, College of Humanities and Science in Al Aflaj, Prince Sattam Bin Abdulaziz University, Saudi Arabia, 11912
6.
Department of Mathematics, College of Sciences and Arts (Muhyil), King Khalied University, Muhyil 61421, Saudi Arabia

Received: 09 April 2023 Revised: 29 May 2023 Accepted: 05 June 2023 Published: 14 June 2023
MSC : 34A07, 34A08, 60G22

In this study, we use the Hilfer derivative to analyze the approximate controllability of fractional stochastic evolution inclusions (FSEIs) with nonlocal conditions. By assuming that the corresponding linear system is approximately controllable, we obtain a novel set of adequate requirements for the approximate controllability of nonlinear FSEIs in meticulous detail. The fixed-point theorem for multi-valued operators and fractional calculus are used to achieve the results. Finally, we use several instances to demonstrate our findings.
- controllability,
- fractional calculus,
- FSD-Inclusions,
- multi-valued maps,
- Hilfer derivative,
- fixed point theory
Citation: Abdelkader Moumen, Ammar Alsinai, Ramsha Shafqat, Nafisa A. Albasheir, Mohammed Alhagyan, Ameni Gargouri, Mohammed M. A. Almazah. Controllability of fractional stochastic evolution inclusion via Hilfer derivative of fixed point theory[J]. AIMS Mathematics, 2023, 8(9): 19892-19912. doi: 10.3934/math.20231014

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Abstract

In this study, we use the Hilfer derivative to analyze the approximate controllability of fractional stochastic evolution inclusions (FSEIs) with nonlocal conditions. By assuming that the corresponding linear system is approximately controllable, we obtain a novel set of adequate requirements for the approximate controllability of nonlinear FSEIs in meticulous detail. The fixed-point theorem for multi-valued operators and fractional calculus are used to achieve the results. Finally, we use several instances to demonstrate our findings.

References

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