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In this article a two-sided variable coefficient fractional diffusionequation (FDE) is investigated, where the variable coefficient occurs outsideof the fractional integral operator. Under a suitable transformation thevariable coefficient equation is transformed to a constant coefficientequation. Then, using the spectral decomposition approach with Jacobipolynomials, we proved the wellposedness of the model and the regularity of itssolution. A spectral approximation scheme is proposed and the accuracy of itsapproximation studied. Two numerical experiments are presented to demonstratethe derived error estimates.

Wellposedness of the two-sided variable coefficient Caputo flux fractional diffusion equation and error estimate of its spectral approximation