Series Solution to Fractional Telegraph Equations Using an Iterative Scheme Based on Yang Transform

In the present paper, an iterative scheme based on Yang transform has been used to obtain series solutions to 1D, 2D and 3D fractional hyperbolic telegraph equations, where the fractional derivative has been considered in Caputo sense. Telegraph equations have been used for describing the distance and time on an electric transmission line with current and voltage, and the fractional variant serves as an extension over the fractional derivative order for these equations. Some preliminaries have been provided, which includes some important results, definitions and Yang transform of some common functions. To demonstrate the efficacy of the proposed scheme, a total of 5 examples have been solved. Comparison between approximate and exact solution at integer order has been provided for 4 out of the 5 examples. The proposed scheme is accurate, robust, and easy to implement, and can potentially be applied to other fractional partial differential equations.