Existence, uniqueness and regularity for a semilinear stochastic subdiffusion with integrated multiplicative noise

IF 2.5 2区数学 Q1 MATHEMATICS

Fractional Calculus and Applied Analysis Pub Date : 2024-02-21 DOI:10.1007/s13540-024-00244-w

Ziqiang Li, Yubin Yan

引用次数: 0

Abstract

We investigate a semilinear stochastic time-space fractional subdiffusion equation driven by fractionally integrated multiplicative noise. The equation involves the \(\psi \)-Caputo derivative of order \(\alpha \in (0,1)\) and the spectral fractional Laplacian of order \(\beta \in (\frac{1}{2},1]\). The existence and uniqueness of the mild solution are proved in a suitable Banach space by using the Banach contraction mapping principle. The spatial and temporal regularities of the mild solution are established in terms of the smoothing properties of the solution operators.

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具有综合乘法噪声的半线性随机子扩散的存在性、唯一性和正则性

我们研究了一个由分数积分乘法噪声驱动的半线性随机时空分数亚扩散方程。该方程涉及阶数为（\alpha \in (0,1)）的卡普托导数和阶数为（\beta \in (\frac{1}{2},1] \）的谱分数拉普拉奇。利用巴拿赫收缩映射原理，在合适的巴拿赫空间中证明了温和解的存在性和唯一性。根据解算子的平滑特性，建立了温和解的空间和时间规律性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Fractional Calculus and Applied Analysis MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

4.70

自引率

16.70%

发文量

101

期刊介绍： Fractional Calculus and Applied Analysis (FCAA, abbreviated in the World databases as Fract. Calc. Appl. Anal. or FRACT CALC APPL ANAL) is a specialized international journal for theory and applications of an important branch of Mathematical Analysis (Calculus) where differentiations and integrations can be of arbitrary non-integer order. The high standards of its contents are guaranteed by the prominent members of Editorial Board and the expertise of invited external reviewers, and proven by the recently achieved high values of impact factor (JIF) and impact rang (SJR), launching the journal to top places of the ranking lists of Thomson Reuters and Scopus.