Optimal Petrov–Galerkin Spectral Approximation Method for the Fractional Diffusion, Advection, Reaction Equation on a Bounded Interval

In this paper we investigate the numerical approximation of fractional diffusion, advection, reaction equation on a bounded interval. Recently explicit form solution to was obtained. Using boundary behavior and Jacobi polynomials, Petrov–Galerkin scheme is proposed analyzed. Numerical experiments are presented which support theoretical results, demonstrate accuracy optimal convergence method.