Positive solutions for boundary value problems of singular fractional differential equations
type: Item
instance of: scholarly article
title: Positive solutions for boundary value problems of singular fractional differential equations
zbMATH Open document ID: 1307.34005
DOI: 10.1155/2013/129640
author: Zhanbing Bai
author: Weichen Sun
author: Weihai Zhang
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: Summary: By using a fixed point theorem, we investigate the existence of a positive solution to the singular fractional boundary value problem \[ {^CD^\alpha_{0+}} u+ f(t,u,{^CD^\nu_{0+}u} {^CD^\mu_{0+}u})+ g(t,u{^CD^\nu_{0+}u}, {^CD^\mu_{0+}u})= 0, \] \[ u(0)= u'(0)= u''(0)= u'''(0)= 0, \] where \(3<\alpha<4\), \(0<\nu< 1\), \(1<\mu<2\), \({^CD^\alpha_{0+}}\) is Caputo fractional derivative, \(f(t,x,y,z)\) is singular at the value \(0\) of arguments \(x\), \(y\), \(z\), and \(g(t,x,y,z)\) satisfies the Lipschitz condition.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6306042
zbMATH Keywords: Caputo fractional derivative
Wikidata QID: Q58915320
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/129640
OpenAlex ID: W2104511073
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description: scientific article; zbMATH DE number 6306042