Approximate controllability of Hilfer fractional neutral stochastic systems of the Sobolev type by using almost sectorial operators

Sivajiganesan Sivasankar; Ramalingam Udhayakumar; Arumugam Deiveegan; Reny George; Ahmed M. Hassan; Sina Etemad; Sivajiganesan Sivasankar; Ramalingam Udhayakumar; Arumugam Deiveegan; Reny George; Ahmed M. Hassan; Sina Etemad

doi:10.3934/math.20231551

AIMS Mathematics

2023, Volume 8, Issue 12: 30374-30404. doi: 10.3934/math.20231551

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Approximate controllability of Hilfer fractional neutral stochastic systems of the Sobolev type by using almost sectorial operators

1.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
2.
Department of Mathematics, Sona College of Technology, Salem 636005, Tamil Nadu, India
3.
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
4.
Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt
5.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran

Received: 25 July 2023 Revised: 07 September 2023 Accepted: 10 September 2023 Published: 08 November 2023
MSC : 34A08, 47H10, 60H10, 93B05

The main aim of this work is to conduct an analysis of the approximate controllability of Hilfer fractional (HF) neutral stochastic differential systems under the condition of an almost sectorial operator with delay. The theoretical ideas linked to stochastic analysis, fractional calculus and semigroup theory, along with the fixed-point technique, are utilized to establish the key results of this article. More precisely, the main theorem of this study is devoted to proving the fact that the relevant linear system is approximately controllable. Finally, to help this research be as comprehensive as possible, we provide a theoretical application and filter system.
- existence,
- approximate controllability,
- Hilfer fractional derivative,
- fixed point theory,
- stochastic system,
- almost sectorial operator
Citation: Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Arumugam Deiveegan, Reny George, Ahmed M. Hassan, Sina Etemad. Approximate controllability of Hilfer fractional neutral stochastic systems of the Sobolev type by using almost sectorial operators[J]. AIMS Mathematics, 2023, 8(12): 30374-30404. doi: 10.3934/math.20231551

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Abstract

The main aim of this work is to conduct an analysis of the approximate controllability of Hilfer fractional (HF) neutral stochastic differential systems under the condition of an almost sectorial operator with delay. The theoretical ideas linked to stochastic analysis, fractional calculus and semigroup theory, along with the fixed-point technique, are utilized to establish the key results of this article. More precisely, the main theorem of this study is devoted to proving the fact that the relevant linear system is approximately controllable. Finally, to help this research be as comprehensive as possible, we provide a theoretical application and filter system.

References

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