Positive solutions of two-point boundary value problems for fractional singular differential equations
type: Item
instance of: scholarly article
title: Positive solutions of two-point boundary value problems for fractional singular differential equations
zbMATH Open document ID: 1263.34009
DOI: 10.1134/S0012266112050011
author: Ravi P. Agarwal
author: Liu Yansheng
author: Donal O'Regan
author: Tian Congcong
published in: Differential Equations
publication date: 2012-11-14T00:00:00Z
review text: The authors consider the fractional singular differential equation \[ D_{0^+}^{\alpha} u(t)+f(t,u(t))=0,\;0<t<1, \] satisfying the conjugate two point boundary conditions \[ u^{(i)}(0)=0,\;0\leq i\leq n-2,\;u(1)=0, \] where \(D_{0^+}^{\alpha}\) is the Riemann-Liouville fractional-order derivative. The authors obtain Green's function for the homogeneous boundary value problem corresponding to the above boundary value problem and establish inequalities involving the Green's function. They prove the existence of twin positive solutions for the two point boundary value problem.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 6105623
zbMATH Keywords: Caputo
zbMATH Keywords: fractional derivative
zbMATH Keywords: boundary value problem
zbMATH Keywords: two-point
zbMATH Keywords: positive solution
reviewed by: K. Rajendra Prasad
MaRDI profile type: Publication
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full work available at URL: s0012266112050011
OpenAlex ID: W2028685401
description: scientific article; zbMATH DE number 6105623