Fractional oscillator equation: analytical solution and algorithm for its approximate computation

被引：16
|
作者：
Blaszczyk, Tomasz [1 ]
Ciesielski, Mariusz [2 ]
机构：
[1] Czestochowa Tech Univ, Inst Math, Al Armii Krajowej 21, PL-42201 Czestochowa, Poland
[2] Czestochowa Tech Univ, Inst Comp & Informat Sci, PL-42201 Czestochowa, Poland
来源：
JOURNAL OF VIBRATION AND CONTROL | 2016年 / 22卷 / 08期
关键词：
Fractional oscillator equation; fractional Euler-Lagrange equation; fractional integral equation; numerical algorithm; EULER-LAGRANGE EQUATIONS; VAN; MECHANICS; CALCULUS; DYNAMICS; MODELS; TERMS;
D O I：
10.1177/1077546314566836
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
In this paper the fractional oscillator equation in a finite time interval is considered. The fractional equation with derivatives of order (0,1] is transformed into its corresponding integral form, by using the symbolic calculus method, in which the binomial expansion of the inverse integral operator is used. A new fractional integral operator is introduced. A numerical algorithm to approximate the solution of the considered equation is proposed. In the final part of this paper examples of numerical solutions of this equation are given.
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页码：2045 / 2052
页数：8
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