MONOTONE ITERATIVE TECHNIQUE FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS

被引：41

作者：

Ramirez, J. D. ^{[1
]}

Vatsala, A. S. ^{[1
]}

机构：

[1] Univ Louisiana Lafayette, Dept Math, Lafayette, LA 70504 USA

来源：

OPUSCULA MATHEMATICA | 2009年 / 29卷 / 03期

关键词：

Riemann-Liouville fractional derivative; monotone method; periodic boundary value problem;

D O I：

10.7494/OpMath.2009.29.3.289

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we develop Monotone Method using upper and lower solutions for fractional differential equations with periodic boundary conditions. Initially we develop a comparison result and prove that the solution of the linear fractional differential equation with periodic boundary condition exists and is unique. Using this we develop iterates which converge uniformly monotonically to minimal and maximal solutions of the nonlinear fractional differential equations with periodic boundary conditions in the weighted norm.

引用

页码：289 / 304

页数：16

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