Positive solutions for multipoint boundary value problem of fractional differential equations
type: Item
instance of: scholarly article
title: Positive solutions for multipoint boundary value problem of fractional differential equations
zbMATH Open document ID: 1223.34008
DOI: 10.1155/2010/601492
author: Wenyong Zhong
published in: Abstract and Applied Analysis
publication date: 2011-02-09T00:00:00Z
full work available at URL: https://eudml.org/doc/231232
review text: The author studies the existence of positive solutions for the boundary value problem \[ \begin{cases} D^{\alpha}u(t)~+~f(t,u(t))~=~0,~~t\in (0,1) \text{~~and~~} \alpha \in(2,3),\\ u(0)~=~u^{\prime}(0)~=~0, ~~~ u^{\prime}(1)~=~\sum_{i=1}^{m-2}~a_i~u^{\prime}(\xi_i).\end{cases}\tag{*} \] He proves in Theorem 3.4 that the problem (*) has at least one positive solution. In Theorem 3.5 he shows, under some additional conditions, that the problem (*) has at least three positive solutions.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B18
zbMATH DE Number: 5848812
zbMATH Keywords: fractional-order differential equations
zbMATH Keywords: positive solution
zbMATH Keywords: boundary-value problem
Wikidata QID: Q58649883
reviewed by: A. M. A. El-Sayed
MaRDI profile type: Publication
OpenAlex ID: W2171685265
cites work: The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
cites work: Inversion theorems for poterntial-type integral transforms in a and onsn-1
cites work: Inversion of integral transform with an extended generalized Mittag-Leffler function
cites work: Existence conditions for a classical solution of the Cauchy problem for the diffusion-wave equation with a partial Caputo derivative
cites work: Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers
cites work: Positive solutions for boundary value problem of nonlinear fractional differential equation
cites work: Q3378412
cites work: Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions
cites work: Boundary value problems for differential equations with fractional order and nonlocal conditions
cites work: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations
cites work: Nonlocal and multiple-point boundary value problem for fractional differential equations
cites work: On positive solutions of a nonlocal fractional boundary value problem
cites work: On the fractional order \(m\)-point boundary value problem in reflexive Banach spaces and weak topologies
cites work: Existence of a positive solution to a class of fractional differential equations
cites work: Positive solutions to singular boundary value problem for nonlinear fractional differential equation
cites work: POSITIVE SOLUTIONS OF NONLOCAL BOUNDARY VALUE PROBLEMS: A UNIFIED APPROACH
cites work: Q5732050
cites work: Q3854213
description: scientific article; zbMATH DE number 5848812