Generalized time-fractional telegrapher’s equation in transmission line modeling

Abstract

An original generalization of telegrapher’s equation is derived by considering the topological generalization of the elementary circuit used in transmission line modeling in order to include the effects of charge accumulation along the line. Also, capacitive and inductive phenomena are assumed to display hereditary effects modeled by the use of fractional calculus. Although developed primarily for transmission lines, the proposed model can be applied to a wider class of diffusion-wave phenomena. The Laplace transform technique is used in obtaining the analytical solution of signal propagation along the line. Several examples illustrate good agreement between results obtained by means of the proposed analytical procedure and numerical techniques for inversion of the Laplace transform.