scholarly journals Iterative Approximation of the Minimal and Maximal Positive Solutions for Multipoint Fractional Boundary Value Problem on an Unbounded Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Guotao Wang ◽  
Sanyang Liu ◽  
Lihong Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Unbounded Domain ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Fractional Boundary Value Problem ◽  
Iterative Approximation ◽  
Monotone Iterative

By employing the monotone iterative method, this paper not only establishes the existence of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain, but also develops two computable explicit monotone iterative sequences for approximating the two positive solutions. An example is given for the illustration of the main result.

scholarly journals Iterative approximation of positive solutions for fractional boundary value problem on the half-line

Filomat ◽  
2018 ◽  
Vol 32 (18) ◽  
pp. 6177-6187 ◽  
Author(s):  
Mourad Chamekh ◽  
Abdeljabbar Ghanmi ◽  
Samah Horrigue
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Fractional Derivative ◽  
Positive Solutions ◽  
Boundary Value ◽  
The Other ◽  
Fractional Boundary Value Problem ◽  
Iterative Approximation ◽  
Derivative Operator ◽  
Liouville Fractional Derivative

In this paper, an iterative method is applied to solve some p-Laplacian boundary value problem involving Riemann-Liouville fractional derivative operator. More precisely, we establish the existence of two positive solutions. Moreover, we prove that these solutions are one maximal and the other is minimal. An example is presented to illustrate our main result. Finally, a numerical method to solve this problem is given.

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

scholarly journals Existence of Positive Solutions for a Nonlinear Higher-Order Multipoint Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min Zhao ◽  
Yongping Sun
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Monotone Iterative Method ◽  
Multipoint Boundary ◽  
Monotone Iterative ◽  
Existence Of Positive Solutions ◽  
Multipoint Boundary Value Problem

We study the existence of positive solutions for a nonlinear higher-order multipoint boundary value problem. By applying a monotone iterative method, some existence results of positive solutions are obtained. The main result is illustrated with an example.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

scholarly journals Existence and Exact Asymptotic Behavior of Positive Solutions for a Fractional Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Habib Mâagli ◽  
Noureddine Mhadhebi ◽  
Noureddine Zeddini
Keyword(s):  
Asymptotic Behavior ◽  
Continuous Function ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Positive Solutions ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Exact Asymptotic Behavior ◽  
Nonnegative Continuous Function

We establish the existence and uniqueness of a positive solution for the fractional boundary value problem , with the condition , where , and is a nonnegative continuous function on that may be singular at or .

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