Solving Time-Fractional Order Telegraph Equation Via Sinc-Legendre Collocation Method

In this paper, we introduce a numerical method for solving time-fractional order telegraph equation. The method depends basically on an expansion of approximated solution in a series of Sinc function and shifted Legendre polynomials. The fractional derivative is expressed in the Caputo definition of fractional derivatives. The expansion coefficients are then determined by reducing the time-fractional order telegraph equation with its boundary and initial conditions to a system of algebraic equations for these coefficients. This system can be solved numerically using the Newton's iteration method. Several numerical examples are introduced to demonstrate the reliability and effectiveness of the introduced method.