Spectral Shifted Jacobi-Gauss-Lobatto Methodology for Solving Two-Dimensional Time-Space Fractional Bioheat Model

In this paper, we extend use the spectral scheme by including a new application for solving the two-dimensional time-space fractional bioheat equation (T-SFBHE) with initial/Neumann boundary conditions. To achieve this goal, we suggest the numerical algorithm that depend on shifted Jacobi-Gauss-Lobatto polynomials (SJ-GL-Ps) together with Jacobi-Gauss-Lobatto points to calculate the approximate derivatives of any order (fractional/ordinary) in the matrix form. the proposed technique of the two examples is applied in order to evidence its utility and precision. The numerical results designate that the utilized approach is very effectual and gives high accuracy and good convergence by using a few grid points.