Eigenvalue problems for fractional ordinary differential equations

被引：45

作者：

Duan, Jun-Sheng ^{[1
,2
]}

Wang, Zhong ^{[3
]}

Liu, Yu-Lu ^{[1
,4
]}

Qiu, Xiang ^{[1
]}

机构：

[1] Shanghai Inst Technol, Coll Sci, Shanghai 201418, Peoples R China

[2] Huaqiao Univ, Inst Math Sci, Quanzhou 362021, Fujian, Peoples R China

[3] Zhaoqing Univ, Dept Math, Zhaoqing 526061, Guang Dong, Peoples R China

[4] Shanghai Univ, Shanghai Inst Appl Math & Mech, Shanghai 200072, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2013年 / 46卷

基金：

中国国家自然科学基金;

关键词：

DIFFUSION;

D O I：

10.1016/j.chaos.2012.11.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The eigenvalue problems are considered for the fractional ordinary differential equations with different classes of boundary conditions including the Dirichlet, Neumann, Robin boundary conditions and the periodic boundary condition. The eigenvalues and eigenfunctions are characterized in terms of the Mittag-Leffler functions. The eigenvalues of several specified boundary value problems are calculated by using MATLAB subroutine for the Mittag-Leffler functions. When the order is taken as the value 2, our results degenerate to the classical ones of the second-ordered differential equations. When the order a satisfies 1 < alpha < 2 the eigenvalues can be finitely many. (C) 2012 Elsevier Ltd. All rights reserved.

引用

页码：46 / 53

页数：8

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