  In this work, we have considered dilaton dark energy model in Weyl-scaled
induced gravitational theory in presence of barotropic fluid. It is to be noted
that the dilaton field behaves as a quintessence. Here we have discussed the
role of dilaton dark energy in modified gravity theories namely, f(R); f(T) and
Horava-Lifshitz gravities and analyzed the behaviour of the dilaton field and
the corresponding potential in respect to these modified gravity theories
instead of Einstein's gravity. In f(R) and f(T) gravities, we have considered
some particular forms of f(R) and f(T) and we have shown that the potentials
always increase with the dilaton fields. But in Horava-Lifshitz gravity, it has
been seen that the potential always decreases as dilation field increases.
