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Fractional partial differential equations are generalisations of classical partial differential equations, which relax the requirement that the derivatives are of integer order. A computational cost inherent to fractional derivatives is their non-local nature, and so they naturally benefit from the global approximation functions that characterise spectral methods. Using Jacobi polynomials integrated under Gaus-sian quadrature, several spectral collocation schemes are developed and tested on afatcat:hmoz4wrvdrch7hykmhjdz2ouuu