A constant enclosure method for validating existence and uniqueness of the solution of an initial value problem for a fractional differential equation

被引：15

作者：

Amairi, M. ^{[1
]}

Aoun, M. ^{[1
]}

Najar, S. ^{[1
]}

Abdelkrim, M. N. ^{[1
]}

机构：

[1] Natl Engn Sch Gabes ENIG, Res Unit Modeling Anal & Control Syst MACS, Gabes, Tunisia

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2010年 / 217卷 / 05期

关键词：

Fractional order differential equations; Caputo fractional derivative; Initial value problems; Existence and uniqueness; Interval analysis; Validated computing;

D O I：

10.1016/j.amc.2010.07.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a new method for validating existence and uniqueness of the solution of an initial value problems for fractional differential equations. An algorithm selecting a stepsize and computing a priori constant enclosure of the solution is proposed. Several illustrative examples, with linear and nonlinear fractional differential equations, are given to demonstrate the effectiveness of the method. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：2162 / 2168

页数：7

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