具有可变指数的时间分数扩散方程的全局存在性和稳定性结果

IF 0.9 Q2 MATHEMATICS

Arabian Journal of Mathematics Pub Date : 2024-06-15 DOI:10.1007/s40065-024-00463-2

Akilandeeswari Aruchamy, Saranya Rayappan, Annapoorani Natarajan

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引用次数: 0

摘要

本文旨在研究带有可变指数源函数的分式偏微分方程的存在性和稳定性结果。在 $α $ -resolvent kernel 和 Schauder -fixed point theorem 的帮助下，建立了 $α \in (0,1)$ 的局部存在性结果。通过定点技术证明了非延续定理，并相应地实现了解的全局存在性。利用收缩原理获得了解的唯一性，并通过皮卡尔算子讨论了乌拉姆-希尔斯和广义乌拉姆-希尔斯-拉西亚斯稳定性概念的稳定性结果。本文还提供了一些示例来说明这些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$Global existence and stability results for a time-fractional diffusion equation with variable exponents$

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Global existence and stability results for a time-fractional diffusion equation with variable exponents

This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for $\alpha \in (0,1)$ is established with the help of the $\alpha $-resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results.

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来源期刊

Arabian Journal of Mathematics MATHEMATICS-

CiteScore

2.20

自引率

8.30%

发文量

审稿时长

13 weeks

期刊介绍： The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics. Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.