  Fractional derivative and delay are important tools in modeling memory
properties in the natural system. This work deals with the stability analysis
of a fractional order delay differential equation \begin{equation*} D^\alpha
x(t)=\delta x(t-\tau)-\epsilon x(t-\tau)^3-px(t)^2+q x(t). \end{equation*} We
provide linearization of this system in a neighbourhood of equilibrium points
and propose linearized stability conditions. To discuss the stability of
equilibrium points, we propose various conditions on the parameters $\delta$,
$\epsilon$, $p$, $q$ and $\tau$. Even though there are five parameters involved
in the system, we are able to provide the stable region sketch in the
$q\delta-$plane for any positive $\epsilon$ and $p$. This provides the complete
analysis of stability of the system. Further, we investigate chaos in the
proposed model. This system exhibits chaos for a wide range of delay parameter.
