Dynamics of the fractional oscillator

被引：121

作者：

Achar, BNN ^{[1
]}

Hanneken, JW ^{[1
]}

Enck, T ^{[1
]}

Clarke, T ^{[1
]}

机构：

[1] Univ Memphis, Memphis, TN 38152 USA

来源：

PHYSICA A | 2001年 / 297卷 / 3-4期

关键词：

Fractional oscillators - Mittag-Leffler functions;

D O I：

10.1016/S0378-4371(01)00200-X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The integral equation of motion of a simple harmonic oscillator is generalized by taking the integral to be of arbitrary order according to the methods of fractional calculus to yield the equation of motion of a fractional oscillator. The solution is obtained in terms of Mittag-Leffler functions using Laplace transforms. The expressions for the generalized momentum and the total energy of the fractional oscillator are also obtained. Numerical application and the phase plane representation of the dynamics are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：361 / 367

页数：7

共 14 条

[1]

[Anonymous], 1995, TRANSFORM METHODS SP

[2]

Arfken GeorgeB., 1995, Mathematical Methods for Physicists, Fourth Edition, VFourth

[3]

BLANK L, 1996, 287 MCCM U MANCH

[4] LINEAR MODELS OF DISSIPATION WHOSE Q IS ALMOST FREQUENCY INDEPENDENT-2 [J].

CAPUTO, M .

GEOPHYSICAL JOURNAL OF THE ROYAL ASTRONOMICAL SOCIETY, 1967, 13 (05) :529-&

[5]

ENCK T, 2000, THESIS U MEMPHIS

[6]

Erdelyi A, 1955, HIGHER TRANSCENDENTA, V3

[7]

FEYNMANN R, 1963, FEYNMANN LECT PHYSIC, V1

[8]

Gorenflo R., 1997, FRACTALS FRACTIONAL

[9]

Kilbas AA, 1993, Fractional Integral and Derivatives: Theory and Applications

[10] Fractional relaxation-oscillation and fractional diffusion-wave phenomena [J].

Mainardi, F .

CHAOS SOLITONS & FRACTALS, 1996, 7 (09) :1461-1477

← 1 2 →