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Attractive Solutions for Hilfer Fractional Neutral Stochastic Integro-Differential Equations with Almost Sectorial Operators

Artificial Intelligence and Mobile Services (AIMS)(2024)

Vellore Inst Technol | Prince Sattam bin Abdulaziz Univ | Thiruvalluvar Univ | Azarbaijan Shahid Madani Univ | King Faisal Univ

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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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Hilfer fractional derivative,stochastic evolution equations,neutral systems,infinite interval,attractivity
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要点】:本文研究了带有几乎扇形算子的无限区间上Hilfer分数中性随机积分-微分方程的吸引解,创新点在于结合了半群理论、随机分析和紧致性方法,以及非紧性测度来建立温和解的存在性和吸引性定理。

方法】:通过运用半群理论、随机分析、紧致性方法和非紧性测度(MNC),在考虑几乎扇形算子的紧致和非紧致性质的基础上,建立了温和解的存在性和吸引性定理。

实验】:本文提供了示例以突出关键发现,但未具体提及实验过程及使用的数据集名称,因此无法概括实验和数据集信息。