Summary: ``In this paper we discuss the relation between non-homogeneous nonlinear fractional diffusive equations and the Schrödinger equation with time-dependent harmonic potential. It is well known that the Cole-Hopf transform allows to linearize non-homogeneous nonlinear diffusive equations (NHNDEs) into a Schrödinger-type equation with time-dependent potential. We first discuss the utility of the results about time-dependent harmonic oscillator to obtain explicit solutions for 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 Schrödinger equation with time-dependent potential. Finally, we apply these results to find explicit solutions to a novel non-homogeneous fractional Burgers-type equation.''