FRACTIONAL MATHIEU EQUATION

摘要

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"+(∮+εcost)x+cDαx=0rnwhere Dax is the order a derivative of x(t), where 0 < a < 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.