正实线上希尔费延迟杜芬问题解的探索

IF 1.7 4区数学 Q1 Mathematics

Boundary Value Problems Pub Date : 2024-07-30 DOI:10.1186/s13661-024-01903-w

Sabri T. M. Thabet, Imed Kedim, Thabet Abdeljawad

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引用次数: 0

摘要

在本文中，我们主要通过无限区间 $(0,\infty )$ 上的 Hilfer 分数导数来研究受电弓类型的时间延迟达芬问题。我们引入了一个在 Mittag-Leffler 函数意义上支持 Bielecki 准则的适当巴拿赫空间，以进行新的和方便的分析。利用经典的定点定理（FPTs）证明了解的存在性和唯一性（$\mathbf{E\&U}$）。此外，我们还讨论了希尔费分数达芬受电弓系统（HFDPS）的海尔-乌兰（HU）稳定性。最后，我们通过提供图形仿真数值示例来检验主要结果的有效性，从而增强了我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Exploring the solutions of Hilfer delayed Duffing problem on the positive real line

In this article, we focus on studying the Duffing problem with the time delay of pantograph type via the Hilfer fractional derivatives on the infinite interval $(0,\infty )$ . An appropriate Banach space supported with the Bielecki norm in the Mittag–Leffler function sense is introduced for new and convenient analysis. The existence and uniqueness ( $\mathbf{E\&U}$ ) of the solutions are proved by utilizing the classical fixed point theorems (FPTs). Moreover, the Hyers–Ulam (HU) stability is discussed for our Hilfer fractional Duffing pantograph system (HFDPS). Ultimately, our results are enhanced by providing numerical examples with graphics simulations to check the validity of the main outcomes.

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来源期刊

Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

4 months

期刊介绍： The main aim of Boundary Value Problems is to provide a forum to promote, encourage, and bring together various disciplines which use the theory, methods, and applications of boundary value problems. Boundary Value Problems will publish very high quality research articles on boundary value problems for ordinary, functional, difference, elliptic, parabolic, and hyperbolic differential equations. Articles on singular, free, and ill-posed boundary value problems, and other areas of abstract and concrete analysis are welcome. In addition to regular research articles, Boundary Value Problems will publish review articles.