Fractional Mathieu Equation

Richard H. Rand, Si M. Sah, Meghan K. Suchorsky
2010 Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise   unpublished
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: 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.
doi:10.1115/detc2010-28068 fatcat:bdotn3pppbf7hhhh4t2o46lpqe