Petrov-Galerkin Lucas Polynomials Procedure for the Time-Fractional Diffusion Equation

Herein, we build and implement a combination of Lucas polynomials basis that fulfills the spatial homogenous boundary conditions. This basis is then used to solve the time-fractional diffusion equation spectrally. The elements of all spectral matrices are explicitly obtained in terms of the Gauss hypergeometric function. The convergence and error analysis of the proposed Lucas expansion is studied. Numerical results indicate the high accuracy and applicability of the suggested algorithm.