TY  - EJOU
AU  - 
T1  - Multi-Order Fractional Mathieu Equation with External Multi-Periodic Excitation
T2  - International Journal of Mathematical Research

PY  - 2016
VL  - 5
IS  - 2
SN  - 2306-2223

AB  - 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).
KW  - Homotopy perturbation method
KW  - Parametric excitation
KW  - Fractional 
calculus
KW  - Harmonic balancing method
KW  - Damping
KW  - Fractional mathieu’s 
equation.
DO  - 10.18488/journal.24/2016.5.2/24.2.166.178