Existence and stability of a q-Caputo fractional jerk differential equation having anti-periodic boundary conditions

IF 1.7 4区 数学 Q1 Mathematics Boundary Value Problems Pub Date : 2024-02-22 DOI:10.1186/s13661-024-01834-6
Khansa Hina Khalid, Akbar Zada, Ioan-Lucian Popa, Mohammad Esmael Samei
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Abstract

In this work, we analyze a q-fractional jerk problem having anti-periodic boundary conditions. The focus is on investigating whether a unique solution exists and remains stable under specific conditions. To prove the uniqueness of the solution, we employ a Banach fixed point theorem and a mathematical tool for establishing the presence of distinct fixed points. To demonstrate the availability of a solution, we utilize Leray–Schauder’s alternative, a method commonly employed in mathematical analysis. Furthermore, we examine and introduce different kinds of stability concepts for the given problem. In conclusion, we present several examples to illustrate and validate the outcomes of our study.
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具有反周期边界条件的 q-Caputo 分数抽搐微分方程的存在性和稳定性
在这项工作中,我们分析了一个具有反周期边界条件的 q 分抽动问题。重点是研究在特定条件下是否存在唯一解并保持稳定。为了证明解的唯一性,我们采用了巴拿赫定点定理和数学工具来确定不同定点的存在。为了证明解的可用性,我们采用了数学分析中常用的 Leray-Schauder 替代法。此外,我们还针对给定问题研究并引入了不同类型的稳定性概念。最后,我们列举了几个例子来说明和验证我们的研究成果。
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来源期刊
Boundary Value Problems
Boundary Value Problems MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
3.00
自引率
5.90%
发文量
83
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.
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