Delannoy Tau-Based Numerical Procedure for the Time-Fractional Cable Model

This study uses the spectral tau method to treat the time-fractional cable equation (TFCE). The proposed algorithm uses the shifted Delannoy polynomials, which are non-symmetric orthogonal. The orthogonality property of the non-symmetric shifted Delannoy polynomials and some representations facilitate obtaining accurate spectral approximations for the TFCE. Several numerical examples ensure the efficiency and accuracy of the method. We compare the suggested scheme to other algorithms and benchmark it against existing analytical solutions to demonstrate the high accuracy of our presented algorithm.