A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative

In this paper, we have presented an accurate and impressive spectral algorithm for solving fractional telegraph equation with Riesz-space derivative and Dirichlet boundary conditions. The proposed method is based on Jacobi tau spectral procedure together with the Jacobi operational matrices of Riemann-Liouville fractional integral and left- and right-sided Caputo fractional derivatives. Primarily, we implement the proposed algorithm in both temporal and spatial discretizations. This algorithm reduces the problem to a system of algebraic equations which considerably simplifies the problem. In addition, an error bound is established in the L 8-norm for the suggested spectral Jacobi tau method. Illustrative examples are included to demonstrate the validity and accuracy of the presented technique.