Numerical solutions to the fractional-order wave equation

New numerical solution to the linear fractional-order wave equation is presented. The Liouville-Caputo sense fractional-derivative operator and Crank-Nicholson finite difference method (CN-FDM) algorithm are employed. The stability of the present technique is considered by the fractional Von Neumann stability analysis method. Special example as an application of the method is provided. The obtained results are examined to check the derived stability condition of the proposed algorithm. Computational results indicate that the present numerical algorithm is efficient and applicable for the problem under study and many other problems.