A comparative study on residual power series method and differential transform method through the time-fractional telegraph equation

Abstract

In the present era of cutting-edge technologies powering electronic devices, energy systems, and modern telecommunication, a mathematical model called the telegraph equation plays a major role. It describes the wave propagation and diffusion processes in a variety of scientific and engineering areas. This work investigates, applies, and compares two semi analytical methods, namely, reduced fractional differential transform method and the Laplace-transformed residual power series method, toward solving the two-dimensional time-fractional telegraph equation. In the recent past, both the methods have been used to solve various linear and non-linear, ordinary, partial, and fractional differential equations. The literature speaks highly about residual power series method being efficient, specially for the non-linear problems. This work puts forth the methodologies and numerical experiments, and it can be observed that both methods result in the same solution for the two-dimensional linear telegraph equation. However, the solutions for the non-linear telegraph equation are better with the differential transform method.

Keywords

• fractional telegraph equation
• fractional reduced differential transform method
• residual power series method
• laplace-transformed residual power series method