  In this paper we discuss the relation between non-homogeneous nonlinear
fractional diffusive equations and the Schrodinger equation with time-dependent
harmonic potential. It is well known that the Cole-Hopf transformation allows
to linearize non-homogeneous nonlinear diffusive equations (NHNDEs) into a
Schrodinger-type equation with time-dependent potential. We first discuss the
utility of the results about time-dependent harmonic oscillator to build
explicit solution of such non-homogeneous nonlinear partial differential
equations. In particular, we recall that starting from a trial polynomial
solution of the NHNDE, it is possible to construct other solutions by using
linear invariants of the Schrodinger equation with time-dependent potential.
Finally we apply these results to find explicit solutions to a novel
non-homogeneous fractional Burgers-type equation.
