ϖ-分式偏微分方程的 Ulam-Hyers-Rassias Mittag-Leffler 稳定性

IF 1.5 3区数学 Q1 MATHEMATICS

Journal of Inequalities and Applications Pub Date : 2024-08-28 DOI:10.1186/s13660-024-03170-w

Mohamed Rhaima, Djalal Boucenna, Lassaad Mchiri, Mondher Benjemaa, Abdellatif Ben Makhlouf

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引用次数: 0

摘要

本文全面分析了ϖ-分式偏微分方程的解表示，尤其侧重于达尔布问题的线性情形。我们展示了ϖ-分式偏微分方程线性情况下达尔布问题的解在连续函数空间中的表示。通过应用广义 Gronwall 不等式，我们建立了连续函数空间中的 Ulam-Hyers-Rassias Mittag-Leffler 稳定性。我们列举了三个数值示例来说明我们结果的有效性和适用性。

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Ulam–Hyers–Rassias Mittag-Leffler stability of ϖ–fractional partial differential equations

This paper offers a comprehensive analysis of solution representations for ϖ-fractional partial differential equations, specifically focusing on the linear case of the Darboux problem. We exhibit a representation of the solutions for the Darboux problem of ϖ-fractional partial differential equations in the linear case in the space of continuous functions. Through the application of the generalized Gronwall inequality, we establish the Ulam–Hyers–Rassias Mittag–Leffler stability in the space of continuous functions. Three numerical examples are presented to show the effectiveness and the applicability of our results.

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来源期刊

Journal of Inequalities and Applications 数学-数学

自引率

6.20%

发文量

136

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.