\((\mathtt{k},\varphi )\)-Hilfer fractional Langevin differential equation having multipoint boundary conditions

IF 1.7 4区 数学 Q1 Mathematics
HuiYan Cheng, Naila, Akbar Zada, Ioan-Lucian Popa, Afef Kallekh
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引用次数: 0

Abstract

The primary objective of this manuscript is to investigate the existence and uniqueness of solutions for the Langevin $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation of different orders with multipoint nonlocal fractional integral boundary conditions. We consider the generalized version of the Hilfer fractional diferential equation called as $(\mathtt{k},\varphi )$ -Hilfer fractional differential equation. We provide some significant outcomes about $(\mathtt{k},\varphi )$ -Hilfer fractional Langevin differential equation that requires deriving equivalent fractional integral equation to $(\mathtt{k},\varphi )$ -Hilfer Langevin fractional differential equation. The existence result is established using the Krasnoselskii’s fixed-point theorem, while the uniqueness is addressed with the help of Banach contraction principle. Additionally, we investigate the different forms of Ulam stability for the solution of the mentioned problem, under specific conditions. To validate our main outcomes, we present a detailed example at the end of the manuscript.
\具有多点边界条件的希尔费分数朗格文微分方程
本手稿的主要目的是研究具有多点非局部分数积分边界条件的不同阶朗格文 $(\mathtt{k},\varphi )$ -Hilfer 分数微分方程解的存在性和唯一性。我们考虑了 Hilfer 分数微分方程的广义版本,称为 $(\mathtt{k},\varphi )$ -Hilfer 分数微分方程。我们提供了一些关于 $(\mathtt{k},\varphi )$ -Hilfer 分式朗格文微分方程的重要结果,这些结果要求推导出与 $(\mathtt{k},\varphi )$ -Hilfer 朗格文分式微分方程等价的分式积分方程。利用克拉斯诺瑟尔斯基定点定理建立了存在性结果,而借助巴拿赫收缩原理解决了唯一性问题。此外,我们还研究了在特定条件下上述问题解的不同形式的乌拉姆稳定性。为了验证我们的主要成果,我们在手稿末尾提供了一个详细的示例。
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
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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