具有混合非局部条件的比例卡普托分数受电弓微分方程的定性分析

Q3 Mathematics Nonlinear Functional Analysis and Applications Pub Date : 2021-02-24 DOI:10.22771/NFAA.2021.26.01.14

Bounmy Khaminsou, Chatthai Thaiprayoon, W. Sudsutad, Sayooj Aby Jose

{"title":"具有混合非局部条件的比例卡普托分数受电弓微分方程的定性分析","authors":"Bounmy Khaminsou, Chatthai Thaiprayoon, W. Sudsutad, Sayooj Aby Jose","doi":"10.22771/NFAA.2021.26.01.14","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.","PeriodicalId":37534,"journal":{"name":"Nonlinear Functional Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"QUALITATIVE ANALYSIS OF A PROPORTIONAL CAPUTO FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION WITH MIXED NONLOCAL CONDITIONS\",\"authors\":\"Bounmy Khaminsou, Chatthai Thaiprayoon, W. Sudsutad, Sayooj Aby Jose\",\"doi\":\"10.22771/NFAA.2021.26.01.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.\",\"PeriodicalId\":37534,\"journal\":{\"name\":\"Nonlinear Functional Analysis and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Functional Analysis and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22771/NFAA.2021.26.01.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Functional Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22771/NFAA.2021.26.01.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 9

摘要

本文研究了Ulam稳定性的存在性、唯一性和四种不同类型，即Ulam-Hiers稳定性、广义Ulam-Hiels稳定性、，一类非线性分数阶受电弓微分方程在混合非局部条件下的比例Caputo分数阶导数解的Ulam-Hiers-Rassias稳定性和广义Ulam-Heers-Rassia斯稳定性。利用著名的经典不动点定理，如Banach收缩原理、Leray Schauder非线性替代和Krasnosel'ski i不动点定理构造了解存在唯一的充分条件。最后，通过两个算例说明了主要结果的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

QUALITATIVE ANALYSIS OF A PROPORTIONAL CAPUTO FRACTIONAL PANTOGRAPH DIFFERENTIAL EQUATION WITH MIXED NONLOCAL CONDITIONS

In this paper, we investigate existence, uniqueness and four different types of Ulam’s stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers- Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and Krasnosel’ski i’s fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Nonlinear Functional Analysis and Applications Mathematics-Analysis

CiteScore

1.90

自引率

0.00%

发文量

期刊介绍： The international mathematical journal NFAA will publish carefully selected original research papers on nonlinear functional analysis and applications, that is, ordinary differential equations, all kinds of partial differential equations, functional differential equations, integrodifferential equations, control theory, approximation theory, optimal control, optimization theory, numerical analysis, variational inequality, asymptotic behavior, fixed point theory, dynamic systems and complementarity problems. Papers for publication will be communicated and recommended by the members of the Editorial Board.