On the propagation of alphabetic-shaped solitons to the (2 + 1)-dimensional fractional electrical transmission line model with wave obliqueness

Abstract

This manuscript deals with the (2 + 1)-dimensional nonlinear electrical transmission line (NETL) equation of fractional-order to explain the dynamics of waves in the nonlinear network lines. The fractional transform with conformable derivative and wave obliqueness is applied to the model equation for converting it into an ordinary differential equation (ODE). To explore alphabetic-shaped solitons, an ansatz and the auxiliary equation methods are utilized to the ODE. The utilized transformation is then put back to the received solutions of the ODE. The solutions of the model equations representing alphabetic solitons are attained in terms of fractionality and wave obliqueness. It is seen that some of the beforehand generated solutions are the particular case of the newly derived solutions. The effects of fractionality, obliqueness, and free parameters on the attained solutions are tested and are demonstrated graphically with physical descriptions. Also, the behavior of the voltage wave propagation of the attained solutions are described. It is found that the alphabetic wave phenomena are changed with the change of obliqueness and fractionality, and the free parameters have substantial effects on the attained solutions. All the attained solitons propagate in the xy-plane as time (t) increases and the soliton propagation is found to be controlled by the free parameters, fractionality, and wave obliqueness. All the reported alphabetic-shaped solitons are found to be new in the sense of conformable derivative, wave obliqueness, and the applied methods.