On the stability and convergence of the time-fractional variable order telegraph equation

In this work, we have generalized the time-fractional telegraph equation using the concept of derivative of fractional variable order. The generalized equation is called time-fractional variable order telegraph equation. This new equation was solved numerically via the Crank–Nicholson scheme. Stability and convergence of the numerical solution were presented in details. Numerical simulations of the approximate solution of the time-fractional variable order telegraph equation were presented for different values of the grid point.