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 is then used to solve time-fractional diffusion equation spectrally. The elements all spectral matrices are explicitly obtained in terms Gauss hypergeometric function. convergence error analysis proposed expansion studied. Numerical results indicate high accuracy applicability suggested algorithm.