含乘性噪声的有限和无限时滞随机分数阶扩散方程

IF 1.1 4区数学 Q2 MATHEMATICS, APPLIED

Asymptotic Analysis Pub Date : 2022-11-16 DOI:10.3233/asy-221811

N. Tuan, T. Caraballo, Tran Ngoc Thach

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引用次数: 0

摘要

在这项工作中，我们研究了具有Caputo–Fabrizio分数导数和乘性噪声的随机分数扩散方程，涉及有限和无限时滞。首先，建立了空间Cp（[-a，b]；Lq（Ω，H*r））和Cδ（（−∞，b]，Lq（ω，H*r））中温和解的存在性和唯一性。接下来，除了研究正则性性质外，我们还分别证明了两种延迟情况下温和解相对于初始函数和分数阶导数的连续性。

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Stochastic fractional diffusion equations containing finite and infinite delays with multiplicative noise

In this work, we investigate stochastic fractional diffusion equations with Caputo–Fabrizio fractional derivatives and multiplicative noise, involving finite and infinite delays. Initially, the existence and uniqueness of mild solution in the spaces C p ( [ − a , b ] ; L q ( Ω , H ˙ r ) ) ) and C δ ( ( − ∞ , b ] ; L q ( Ω , H ˙ r ) ) ) are established. Next, besides investigating the regularity properties, we show the continuity of mild solutions with respect to the initial functions and the order of the fractional derivative for both cases of delay separately.

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来源期刊

Asymptotic Analysis 数学-应用数学

CiteScore

1.90

自引率

7.10%

发文量

审稿时长

6 months

期刊介绍： The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand. Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.