Attractive solutions for Hilfer fractional neutral stochastic integro-differential equations with almost sectorial operators

Sivajiganesan Sivasankar; Ramalingam Udhayakumar; Abd Elmotaleb A.M.A. Elamin; R. Samidurai; Sina Etemad; Muath Awadalla; Sivajiganesan Sivasankar; Ramalingam Udhayakumar; Abd Elmotaleb A.M.A. Elamin; R. Samidurai; Sina Etemad; Muath Awadalla

doi:10.3934/math.2024564

AIMS Mathematics

2024, Volume 9, Issue 5: 11486-11510. doi: 10.3934/math.2024564

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Attractive solutions for Hilfer fractional neutral stochastic integro-differential equations with almost sectorial operators

1.
Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, Tamil Nadu, India
2.
Department of Mathematics, College of Science and Humanity, Prince Sattam bin Abdulaziz University, Sulail, Al-Kharj 11942, Saudi Arabia
3.
Department of Mathematics, Thiruvalluvar University, Serkkadu, Vellore 632115, Tamil Nadu, India
4.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
5.
Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq
6.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia

Received: 26 January 2024 Revised: 02 March 2024 Accepted: 13 March 2024 Published: 25 March 2024
MSC : 26A33, 34A12, 37L05, 60H10

This paper studies the integro-differential equations of Hilfer fractional (HF) neutral stochastic evolution on an infinite interval with almost sectorial operators and their attractive solutions. We use semigroup theory, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. We establish the existence and attractivity theorems for mild solutions by considering the fact that the almost sectorial operator is both compact and noncompact. Example that highlight the key findings are also provided.
- Hilfer fractional derivative,
- stochastic evolution equations,
- neutral systems,
- infinite interval,
- attractivity
Citation: Sivajiganesan Sivasankar, Ramalingam Udhayakumar, Abd Elmotaleb A.M.A. Elamin, R. Samidurai, Sina Etemad, Muath Awadalla. Attractive solutions for Hilfer fractional neutral stochastic integro-differential equations with almost sectorial operators[J]. AIMS Mathematics, 2024, 9(5): 11486-11510. doi: 10.3934/math.2024564

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Abstract

This paper studies the integro-differential equations of Hilfer fractional (HF) neutral stochastic evolution on an infinite interval with almost sectorial operators and their attractive solutions. We use semigroup theory, stochastic analysis, compactness methods, and the measure of noncompactness (MNC) as the foundation for our methodologies. We establish the existence and attractivity theorems for mild solutions by considering the fact that the almost sectorial operator is both compact and noncompact. Example that highlight the key findings are also provided.

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