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Fractional Mathieu equation
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DOI：10.1016/j.cnsns.2009.12.009.png)
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Abstract
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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-n + (delta + epsilon cost)x + cD(alpha)x = 0 where D(x)x is the order 7 derivative of x(t), where 0 < alpha < 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 (C) 2009 Elsevier B.V All rights reserved
Keywords:
Fractional calculus
Fractional derivative
Parametric excitation
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