Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation
type: Item
instance of: scholarly article
title: Monotone iterative solutions for nonlinear boundary value problems of fractional differential equation
zbMATH Open document ID: 1291.34014
DOI: 10.1155/2013/493164
author: Chaozhu Hu
author: Songfa Xie
author: Bin Liu
published in: Abstract and Applied Analysis
publication date: 2014-06-23T00:00:00Z
review text: Summary: By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 6306881
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/493164
OpenAlex ID: W1980158241
Wikidata QID: Q58916888
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: Q3408155
cites work: On the numerical solution of fractional Sturm–Liouville problems
cites work: Analytical approach to linear fractional partial differential equations arising in fluid mechanics
cites work: Decomposition method for solving fractional Riccati differential equations
cites work: A collocation-shooting method for solving fractional boundary value problems
cites work: EXISTENCE RESULTS FOR FRACTIONAL BOUNDARY VALUE PROBLEM VIA CRITICAL POINT THEORY
cites work: Existence of solutions for a class of fractional boundary value problems via critical point theory
cites work: Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations
cites work: Upper and lower solutions method for impulsive partial hyperbolic differential equations with fractional order
cites work: The method of upper and lower solutions and impulsive fractional differential inclusions
cites work: Upper and lower solutions method and a fractional differential equation boundary value problem
cites work: Monotone iterative technique for boundary value problems of a nonlinear fractional differential equation with deviating arguments
cites work: Monotone iterative sequences for nonlinear boundary value problems of fractional order
cites work: Q3996430
description: scientific article; zbMATH DE number 6306881