Damped oscillations in view of the fractional oscillator equation
Damped oscillations in view of the fractional oscillator equation
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DOI：
10.1103/physrevb.66.184201
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发表时间：
2002-11
影响因子：
3.7
通讯作者：
Y. Ryabov;A. Puzenko
中科院分区：
文献类型：
--
作者：
Y. Ryabov;A. Puzenko
讨论了含分数阶时间导数的Riemann-Liouville型分数阶振子方程。得到了分数阶振子方程的精确解。在此基础上，建立了分数阶时间导数与耗散性质之间的对应关系。导出了分数阶时间导数的阶数与耗散常数之间的关系。除了精确解外，还发展了摄动方法。结果表明，摄动法和精确解得到了相似的结果。在精确解的基础上，阐述了分数时间演化的概念。
This paper discusses the fractional oscillator equation involving fractional time derivatives of the Riemann-Liouville type. The exact solution of the fractional oscillator equation was obtained. On this basis the correspondence between the fractional time derivative and the dissipative properties was established. The relationship between the order of the fractional time derivative and the dissipative constant was derived. In addition to the exact solution, the perturbation approach was developed as well. It was shown that the perturbation method and exact solution lead to similar results. On the basis of the exact solution, the concept of fractional time evolution was illustrated.