Positive solutions for singular fractional differential equations with three-point boundary conditions

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• 作者：Bingxian Li ; Shurong Sun ; Zhenlai Han
• 关键词：Fractional differential equations ; Existence and multiplicity ; Singular boundary value problem ; Positive solution
• 刊名：Journal of Applied Mathematics and Computing
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：52
• 期：1-2
• 页码：477-488
• 全文大小：391 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Computational Mathematics and Numerical Analysis
  Applied Mathematics and Computational Methods of Engineering
  Theory of Computation
  Mathematics of Computing
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1865-2085
• 卷排序：52

文摘

In this paper, we consider the nonlinear three-point boundary value problem of singular fractional differential equations $$\begin{aligned} D^{\alpha }_{0^+}u(t)+a(t)f(t,u(t))=0,\quad 0<t<1,\;2<\alpha \le 3 \end{aligned}$$with boundary conditions $$\begin{aligned}u(0)=0,\quad D^{\beta }_{0^+}u(0)=0,\quad D^{\beta }_{0^{+}}u(1)=bD^{\beta }_{0^{+}}u(\xi ),\quad 1\le \beta \le 2 \end{aligned}$$involving Riemann–Liouville fractional derivatives \(D^{\alpha }_{0^{+}}\) and \(D^{\beta }_{0^{+}}\). The nonlinear term f permits singularities with respect to both the time and space variables. We obtain several local existence and multiplicity of positive solutions theorems by introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions. An example is given to show the applicability of our main results.KeywordsFractional differential equationsExistence and multiplicity Singular boundary value problemPositive solutionMathematics Subject Classification34A0834B1634B18References1.Oldham, K., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)MATHGoogle Scholar2.Miller, K., Ross, B.: An Introduction to the Fractional Calculus and Fractional Differential Equation. Wiley, New York (1993)MATHGoogle Scholar3.Podlubny, I.: Fractional Differential Equations. Academic Press, New York (1999)MATHGoogle Scholar4.Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Applications of Fractional Differential Equations. The Netherlands, Amsterdam (2006)MATHGoogle Scholar5.Samko, S., Kilbas, A., Marichev, O.: Fractional Integral and Derivative. Theory and Applications. Gordon and Breach, Switzerland (1993)MATHGoogle Scholar6.Zeidler, E.: Nonlinear Functional Analysis and its Applications I: Fixed-Point Theorems, Berlin. 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Academic Press, San Diego (1988)MATHGoogle ScholarCopyright information© Korean Society for Computational and Applied Mathematics 2015Authors and AffiliationsBingxian Li1Shurong Sun1Zhenlai Han1Email author1.School of Mathematical SciencesUniversity of JinanJinanPeople’s Republic of China About this article CrossMark Print ISSN 1598-5865 Online ISSN 1865-2085 Publisher Name Springer Berlin Heidelberg About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s12190-015-0950-2_Positive solutions for singular fr", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s12190-015-0950-2_Positive solutions for singular fr", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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