非局部初始条件下分数阶积分微分扩散方程的温和解

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-10-27 DOI:10.3390/fractalfract7110785

Jia Mu, Zhiyuan Yuan, Yong Zhou

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引用次数: 0

摘要

分数阶积分微分扩散方程在描述异常扩散现象方面起着重要作用。本文研究了这些方程温和解的存在唯一性。首先，我们构造了一个合适的解析族，利用拉普拉斯变换的卷积定理、概率密度函数、柯西积分公式和富比尼定理研究了相关的等连续性、强连续性和紧性性质。然后，对所考虑的方程构造一个合理的温和解。最后，利用不动点定理，得到了所考虑方程温和解存在唯一性的充分条件。

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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Mild Solutions of Fractional Integrodifferential Diffusion Equations with Nonlocal Initial Conditions via the Resolvent Family

Fractional integrodifferential diffusion equations play a significant role in describing anomalous diffusion phenomena. In this paper, we study the existence and uniqueness of mild solutions to these equations. Firstly, we construct an appropriate resolvent family, through which the related equicontinuity, strong continuity, and compactness properties are studied using the convolution theorem of Laplace transform, the probability density function, the Cauchy integral formula, and the Fubini theorem. Then, we construct a reasonable mild solution for the considered equations. Finally, we obtain some sufficient conditions for the existence and uniqueness of mild solutions to the considered equations by some fixed point theorems.

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来源期刊

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.