On the traveling waves in nonlinear electrical transmission lines with intrinsic fractional-order using discrete tanh method

Abstract

Abstract In this paper we investigate the solutions of the fractional partial differential-difference equations governing the dynamics of the voltage wave flowing inside two fractional (low pass and pass band) nonlinear electrical transmission lines (NETL). Through the discrete Tanh method, we derive the traveling wave solutions i.e (kink, dark, singular kink solitons) of two fractional partial differential-difference equations by using the fractional complex transform. The impact of the fractional order on the dynamical behavior of the analytical solutions in both models is highlighted. From our findings the perfect matching between the analytical and the numerical solutions is justified by the stability seen as the resulting wave propagates safely inside the fractional low pass NETL including real inductor. We get for the fractional pass band NETL a rise of nonlinear periodic waves and a train of multi periodic solitons during the numerical simulations. We show that, according to the modified Riemann–Liouville derivative properties, the findings can describe physical systems such as electrical systems and nonlinear electrical transmission lines with transient effect.