Haniye Hajinezhad - Department of Mathematics, Payame Noor University, Tehran, Iran
Ali R. Soheili - Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

In this paper, a two-dimensional time-fractional telegraph equation is considered with derivative in the sense of Caputo and ۱<\beta<۲. The aim of this work is to extend the Crank--Nicolson method for this time-fractional telegraph equation. The stability and convergence of the numerical method are investigated. Also, the accuracy and efficiency of the proposed method are demonstrated by numerical experiments.

Time-Fractional Telegraph Equation, Crank-Nicolson Method, Stability, Convergence