Fractional Mathieu Equation
Fractional Mathieu Equation
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DOI：
10.1115/detc2010-28068
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发表时间：
2010-11
期刊：
影响因子：
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通讯作者：
R. Rand;S. Sah;M. K. Suchorsky
中科院分区：
文献类型：
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作者：
R. Rand;S. Sah;M. K. Suchorsky
在回顾了分数阶导数的概念后，我们推导了 ODE 中将稳定区域与不稳定区域分开的过渡曲线表达式：x″ + (δ + ecost)x + cDαx = 0，其中 Dα x 是 x(t) 的 α 阶导数，其中 0 < α < 1。我们使用调和平衡方法，获得 n = 1 过渡曲线的最低阶近似值和高阶近似值。我们还获得了 n = 0 过渡曲线的表达式。版权所有 © 2010 ASME
After reviewing the concept of fractional derivative, we derive expressions for the transition curves separating regions of stability from regions of instability in the ODE: x″ + (δ + ecost)x + cDαx = 0 where Dα x is the order α derivative of x(t), where 0 < α < 1. We use the method of harmonic balance and obtain both a lowest order approximation as well as a higher order approximation for the n = 1 transition curves. We also obtain an expression for the n = 0 transition curves.Copyright © 2010 by ASME