Abstract: Fractional-order telegraph equation is regarded as one of most important equations in communication engineering, which is hard to obtain the analytical solution, so it is crucial to study the numerical methods. In order to obtain the numerical solutions of fractional-order telegraph equations, this study derives the corresponding differential operational matrix through Chebyshev polynomials. Furthermore, the nonlinear telegraph equation is transformed into the system of algebra equations with known coefficients. Then, the numerical solutions can be obtained by solving the system. Lastly, the numerical example is proposed to verify the feasibility and effectiveness.

Key words: Chebyshev polynomials, fractional-order telegraph equations, numerical solutions, Tau method