Stability Analysis of Fractional-Order Mathieu Equation with Forced Excitation

The advantage of fractional-order derivative has attracted extensive attention in the field dynamics. In this paper, we investigated stability Mathieu equation under forced excitation, which is based on a model pantograph–catenary system. First, obtained approximate analytical expressions and periodic solutions boundaries by multi-scale method perturbation method, correctness these results were verified through numerical analysis Matlab. addition, analyzing k’T-periodic system, existence unstable k’T-resonance lines simulation, visually effect system parameters. show that excitation with finite period does not change position boundaries, but it can affect solutions. Moreover, properties resonant lines, found when points perturbed same frequency became due to resonance. Finally, both damping coefficient parameters have important influences resonance lines.