Existence and exact asymptotic behavior of positive solutions for a fractional boundary value problem
type: Item
instance of: scholarly article
title: Existence and exact asymptotic behavior of positive solutions for a fractional boundary value problem
zbMATH Open document ID: 1274.34068
DOI: 10.1155/2013/420514
author: Habib Mâagli
author: Noureddine Mhadhebi
author: Noureddine Zeddini
published in: Abstract and Applied Analysis
publication date: 2013-05-08T00:00:00Z
review text: Summary: We establish the existence and uniqueness of a positive solution \(u\) for the fractional boundary value problem \(D^\alpha u(x) = -a(x)u^\sigma(x), x \in (0, 1)\) with the condition \(\lim_{x \to 0}D^{\alpha -1} u(x) = 0, u(1) = 0\), where \(1 < \alpha \leq 2, \sigma \in (-1, 1)\) and \(a\) is a nonnegative continuous function on \((0, 1)\) that may be singular at \(x = 0\) or \(x = 1\).
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 34A08
zbMATH DE Number: 6161332
Wikidata QID: Q58916243
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/420514
OpenAlex ID: W2045164504
cites work: Q5699297
cites work: Global existence theory and chaos control of fractional differential equations
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations
cites work: Q3080075
cites work: Positive solutions for boundary value problem of nonlinear fractional differential equation
cites work: Existence of solutions for irregular boundary value problems of nonlinear fractional differential equations
cites work: Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions
cites work: Positive solutions for a class of singular fractional boundary value problems
cites work: Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations
cites work: A singular boundary value problem for nonlinear differential equations of fractional order
cites work: A sufficient condition for the existence of a positive solution for a nonlinear fractional differential equation with the Riemann-Liouville derivative
cites work: Q3630717
cites work: Positive solutions to boundary value problems of nonlinear fractional differential equations
cites work: Regular variation and differential equations
cites work: Regularly varying functions
description: scientific article; zbMATH DE number 6161332