Analysis of impulsive Caputo fractional integro-differential equations with delay

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-09-03 DOI:10.1002/mma.10426

Akbar Zada, Usman Riaz, Junaid Jamshed, Mehboob Alam, Afef Kallekh

引用次数: 0

Abstract

The main focus of this manuscript is to study an impulsive fractional integro-differential equation with delay and Caputo fractional derivative. The existence solution of such a class of fractional differential equations is discussed for linear and nonlinear case with the help of direct integral method. Moreover, Banach's fixed point theorem and Schaefer's fixed point theorem are use to discuss the uniqueness and at least one solution of the said fractional differential equations, respectively. Some hypothesis and inequalities are utilize to present four different types of Hyers–Ulam stability of the mentioned impulsive integro-differential equation. Example is provide for the illustration of main results.

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有延迟的脉冲卡普托分数积分微分方程的分析

本手稿的重点是研究具有延迟和卡普托分数导数的脉冲分数积分微分方程。在直接积分法的帮助下，讨论了这类分数微分方程在线性和非线性情况下的存在解。此外，还利用巴纳赫定点定理和谢弗定点定理分别讨论了上述分数微分方程的唯一性和至少一个解。利用一些假设和不等式提出了上述脉冲积分微分方程的四种不同类型的 Hyers-Ulam 稳定性。为说明主要结果还提供了实例。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.