Fractional Mathieu equation

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 + ϵ cos t ) x + cD α x = 0 where D α 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.