Time fractional telegraph equation and its solution by Laplace transform method

Abstract

In this paper, one-dimensional time fractional telegraph equation is deduced using fractional Ohm’s law in transmission lines. The nonlocal behavior, arising from the time fractality, is discussed via fractional calculus. Here, the time fractional differential equation related to electrical GLRC circuit is proposed in terms of the Liouville–Caputo fractional derivative. To keep the dimensionality of the physical parameters [Formula: see text] the new parameter [Formula: see text] is introduced. This parameter ([Formula: see text]) characterizes the existence of fractional structure in the system. The analytical solution of the proposed equation is obtained by using Laplace transform method in terms of Mittag-Leffler function which describes physical system with memory. The order of the time derivative being considered is [Formula: see text]. The result of an example shows that the behavior of voltage depends on the value of the fractional order of the proposed equation.