Monotone iterative sequences for nonlinear boundary value problems of fractional order

被引：79

作者：

Al-Refai, Mohammed ^{[1
]}

Hajji, Mohamed Ali ^{[1
]}

机构：

[1] United Arab Emirates Univ, Dept Math Sci, Al Ain, U Arab Emirates

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 11期

关键词：

Fractional differential equations; Boundary value problems; Maximum principle; Lower and upper solutions; Caputo fractional derivative;

D O I：

10.1016/j.na.2011.03.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we extend the maximum principle and the method of upper and lower solutions to boundary value problems with the Caputo fractional derivative. We establish positivity and uniqueness results for the problem. We then introduce two well-defined monotone sequences of upper and lower solutions which converge uniformly to the actual solution of the problem. A numerical iterative scheme is introduced to obtain an accurate approximate solution for the problem. The accuracy and efficiency of the new approach are tested through two examples. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3531 / 3539

页数：9

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