The Periodic Solution of Fractional Oscillation Equation with Periodic Input

被引：15

作者：

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

机构：

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

[2] Zhaoqing Univ, Sch Math & Informat Sci, Zhaoqing 526061, Guangdong, Peoples R China

来源：

ADVANCES IN MATHEMATICAL PHYSICS | 2013年 / 2013卷

基金：

中国国家自然科学基金;

关键词：

DIFFERENTIAL-EQUATIONS; EXISTENCE; SYSTEM;

D O I：

10.1155/2013/869484

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The periodic solution of fractional oscillation equation with periodic input is considered in this work. The fractional derivative operator is taken as D--infinity(t)alpha, where the initial time is -infinity; hence, initial conditions are not needed in the model of the present fractional oscillation equation. With the input of the harmonic oscillation, the solution is derived to be a periodic function of time t with the same circular frequency as the input, and the frequency of the solution is not affected by the system frequency c as is affected in the integer-order case. These results are similar to the case of a damped oscillation with a periodic input in the integer-order case. Properties of the periodic solution are discussed, and the fractional resonance frequency is introduced.

引用

页数：6

共 33 条

[1] Response characteristics of a fractional oscillator [J].