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Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation

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  • Joshua Ikechukwu Nwamba

Abstract

This paper presents an investigation of the behavior of the multi-order fractional differential equation (MFDE). We derive expressions for the transition curves separating regions of stability from instability for the MFDE generally and the particular case K=2. Employing the harmonic balance technique, we obtained approximate expressions for the n=1 and n=2 transition curves of the MFDE and particularly for the case k=2. We also obtained an approximate analytical solution to the multi-order fractionally damped and forced Duffing-Mathieu equation as well as some special cases computationally using the Homotopy Perturbation Method (HPM).

Suggested Citation

  • Joshua Ikechukwu Nwamba, 2016. "Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation," International Journal of Mathematical Research, Conscientia Beam, vol. 5(2), pages 166-178.
    • Handle: RePEc:pkp:ijomre:v:5:y:2016:i:2:p:166-178:id:2194
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