Abstract
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. Three numerical experiments are presented to demonstrate the derived error estimates.
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