Existence and uniqueness of solutions of initial value problems for nonlinear langevin equation involving two fractional orders

被引：90

作者：

Yu, Tao ^{[1
]}

Deng, Ke ^{[1
]}

Luo, Maokang ^{[1
]}

机构：

[1] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2014年 / 19卷 / 06期

关键词：

Fractional Langevin equation; Caputo fractional derivative; Initial value problem; Existence and uniqueness; Fixed point;

D O I：

10.1016/j.cnsns.2013.09.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The solvability of initial value problems for nonlinear Langevin equation involving two fractional orders are discussed in this paper. An existence result for the solution is obtained using the Leray-Schauder nonlinear alternative. In addition, sufficient conditions for unique solution are established under the Banach contraction principle. The existence results for the initial value problems of nonlinear classical Langevin equation follow as a special case of our results. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：1661 / 1668

页数：8

共 22 条

[1] A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions [J].

Agarwal, Ravi P. ;

Benchohra, Mouffak ;

Hamani, Samira .

ACTA APPLICANDAE MATHEMATICAE, 2010, 109 (03) :973-1033

[2] A study of nonlinear Langevin equation involving two fractional orders in different intervals [J].

Ahmad, Bashir ;

Nieto, Juan J. ;

Alsaedi, Ahmed ;

El-Shahed, Moustafa .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2012, 13 (02) :599-606

[3] Solvability of Nonlinear Langevin Equation Involving Two Fractional Orders with Dirichlet Boundary Conditions [J].

Ahmad, Bashir ;

Nieto, Juan J. .

INTERNATIONAL JOURNAL OF DIFFERENTIAL EQUATIONS, 2010, 2010

[4]

[Anonymous], ANOMALOUS TRANSPORT

[5]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[6] Existence results for fractional impulsive integrodifferential equations in Banach spaces [J].

Balachandran, K. ;

Kiruthika, S. ;

Trujillo, J. J. .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2011, 16 (04) :1970-1977

[7] Critical exponent of the fractional Langevin equation [J].

Burov, S. ;

Barkai, E. .

PHYSICAL REVIEW LETTERS, 2008, 100 (07)

[8] On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator [J].

Camargo, R. Figueiredo ;

de Oliveira, E. Capelas ;

Vaz, J., Jr. .

JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (12)

[9]

Coffey W. T., 2004, The Langevin Equation

[10] Existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations [J].

Deng, Jiqin ;

Ma, Lifeng .

APPLIED MATHEMATICS LETTERS, 2010, 23 (06) :676-680

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