Pell-Lucas Discretization Method for Finding the Solution of Caputo-Fabrizio Time-Fractional Diffusion Equations

A novel numerical algorithm based on Pell-Lucas polynomials is introduced for solving Caputo-Fabrizio time-fractional diffusion equations. The proposed method is provided with the help of modified operational matrices, which these matrices are computed with the high precision algorithm. Also, the Pell-Lucas polynomials and their properties have great importance in our scheme. It is worth noting that the accuracy of these matrices is very effective in the accuracy of the calculation process of the approximate solution. Besides of numerical approach, we discuss error estimation and convergence of approximate solution to exact solution. At last, to demonstrate the conspicuous role of the method and the operational matrices, we examine several numerical examples.