  In this article a two-sided variable coefficient fractional diffusion
equation (FDE) is investigated, where the variable coefficient occurs outside
of the fractional integral operator. Under a suitable transformation the
variable coefficient equation is transformed to a constant coefficient
equation. Then, using the spectral decomposition approach with Jacobi
polynomials, we proved the wellposedness of the model and the regularity of its
solution. A spectral approximation scheme is proposed and the accuracy of its
approximation studied. Two numerical experiments are presented to demonstrate
the derived error estimates.
