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

Joshua Ikechukwu Nwamba

International Journal of Mathematical Research, 2016, vol. 5, issue 2, 166-178

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).

Keywords: Homotopy perturbation method; Parametric excitation; Fractional calculus; Harmonic balancing method; Damping; Fractional mathieu’s equation (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

Downloads: (external link)
https://archive.conscientiabeam.com/index.php/24/article/view/2194/3216 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:pkp:ijomre:v:5:y:2016:i:2:p:166-178:id:2194

Access Statistics for this article

More articles in International Journal of Mathematical Research from Conscientia Beam
Bibliographic data for series maintained by Dim Michael ().