On the Numerical Solutions for the Time-Fractional Telegraph Equation

Fractional differential equations have recently been applied in various area of engineering, science, finance, applied mathematics, bio-engineering and others.In this paper, an efficient numerical method for solving telegraph equation with fractional time derivative ? (1 < ? ? 2) , is proposed. The fractional derivative is described in the Caputo sense. This technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.