Sequential fractional differential equations with three-point boundary conditions

被引：95

作者：

Ahmad, Bashir ^{[2
]}

Nieto, Juan J. ^{[1
,2
]}

机构：

[1] Univ Santiago de Compostela, Fac Matemat, Dept Anal Matemat, Santiago De Compostela 15782, Spain

[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2012年 / 64卷 / 10期

关键词：

Differential equation; Fractional order; Three-point boundary conditions; Existence; Fixed point; EXISTENCE;

D O I：

10.1016/j.camwa.2012.02.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies a nonlinear three-point boundary value problem of sequential fractional differential equations of order alpha + 1 with 1 < alpha <= 2. The expression for Green's function of the associated problem involving the classical gamma function and the generalized incomplete gamma function is obtained. Some existence results are obtained by means of Banach's contraction mapping principle and Krasnoselskii's fixed point theorem. An illustrative example is also presented. Existence results for a three-point third-order nonlocal boundary value problem of nonlinear ordinary differential equations follow as a special case of our results. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：3046 / 3052

页数：7

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