A study of nonlinear Langevin equation involving two fractional orders in different intervals

被引：237

作者：

Ahmad, Bashir ^{[1
]}

Nieto, Juan J. ^{[2
]}

Alsaedi, Ahmed ^{[1
]}

El-Shahed, Moustafa ^{[3
]}

机构：

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

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

[3] Qasssim Univ, Dept Math, Coll Educ, Qasssim, Saudi Arabia

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2012年 / 13卷 / 02期

关键词：

Langevin equation; Fractional order; Three-point boundary conditions; Existence; Fixed point; ANOMALOUS DIFFUSION; EXISTENCE; RIEMANN;

D O I：

10.1016/j.nonrwa.2011.07.052

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper studies a nonlinear Langevin equation involving two fractional orders alpha is an element of (0, 1] and beta is an element of (1, 2] with three-point boundary conditions. The contraction mapping principle and Krasnoselskii's fixed point theorem are applied to prove the existence of solutions for the problem. The 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. Some illustrative examples are also discussed. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：599 / 606

页数：8

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