Existence of Solutions for Riemann-Liouville Fractional Dirichlet Boundary Value Problem

IF 1.4 4区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Iranian Journal of Science and Technology, Transactions A: Science Pub Date : 2024-11-05 DOI:10.1007/s40995-024-01696-8
Zhiyu Li
{"title":"Existence of Solutions for Riemann-Liouville Fractional Dirichlet Boundary Value Problem","authors":"Zhiyu Li","doi":"10.1007/s40995-024-01696-8","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, existence theorems of solutions for the Riemann-Liouville fractional Dirichlet</p><p>boundary value problem <span>\\(\\begin{aligned} \\left\\{ \\begin{aligned} {D_{0+}^{\\alpha }}x(t)=f\\left( t,x(t),{D_{0+}^{\\alpha -1}}x(t)\\right) , \\ t\\in (0,1),\\\\ x(0)=0, \\ x(1)=B, \\end{aligned}\\right. \\end{aligned}\\)</span>are obtained, where <span>\\(B\\in {\\mathbb {R}}\\)</span>, <span>\\({D_{0+}^{\\alpha }}x(t)\\)</span> is the Riemann-Liouville fractional derivative, <span>\\({\\alpha }\\in (1,2]\\)</span> is a real number, and <span>\\(f\\in C\\left( [0,1]\\times {\\mathbb {R}}^{2}, {\\mathbb {R}}\\right)\\)</span>. We do not impose growth restrictions on nonlinear term <i>f</i> as many authors do but merely require that <i>f</i> satisfies sign conditions at the origin. Our analysis is based on the nonlinear alternative of Leray-Schauder. Finally, we provide an example to verify our main results.</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"49 1","pages":"161 - 167"},"PeriodicalIF":1.4000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-024-01696-8","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper, existence theorems of solutions for the Riemann-Liouville fractional Dirichlet

boundary value problem \(\begin{aligned} \left\{ \begin{aligned} {D_{0+}^{\alpha }}x(t)=f\left( t,x(t),{D_{0+}^{\alpha -1}}x(t)\right) , \ t\in (0,1),\\ x(0)=0, \ x(1)=B, \end{aligned}\right. \end{aligned}\)are obtained, where \(B\in {\mathbb {R}}\), \({D_{0+}^{\alpha }}x(t)\) is the Riemann-Liouville fractional derivative, \({\alpha }\in (1,2]\) is a real number, and \(f\in C\left( [0,1]\times {\mathbb {R}}^{2}, {\mathbb {R}}\right)\). We do not impose growth restrictions on nonlinear term f as many authors do but merely require that f satisfies sign conditions at the origin. Our analysis is based on the nonlinear alternative of Leray-Schauder. Finally, we provide an example to verify our main results.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
4.00
自引率
5.90%
发文量
122
审稿时长
>12 weeks
期刊介绍: The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences
期刊最新文献
Existence of Solutions for Riemann-Liouville Fractional Dirichlet Boundary Value Problem Exploration of Photoactive Cd2+ Substitutions on V2O5 Nanoparticles and Their Catalytic Potential Against the Toxic Dye Cylindrical Gravastar Structure in Energy–momentum Squared Gravity DNAzyme Loaded Nano-Niosomes Confer Anti-Cancer Effects in the Human Breast Cancer MCF-7 Cells by Inhibiting Apoptosis, Inflammation, and c-Myc/cyclin D1 Approximation by Generalised Szász-type Operators based on Appell Polynomials
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1