This paper presents a novel investigation into the dynamics of the time delayed Mathieu equation with fractional order damping given by equation (7). We employed the approximate technique, Adomian Decoposition Method (ADM) in obtaining an analytical result which agreed excellently with the series solution of the above mentioned delay differential equation (DDE) also obtained in this paper. We considered some insightful examples too. It was observed that the ADM gives a solution that is more compact and converges faster when compared to the series solution obtained. Moreover the ADM does not involve tedious calculations and is easier to handle compared to the series method which may become demanding at some point especially if nonlinearity is introduced.
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