On Alphabetical Shaped Soliton for Intrinsic Fractional Coupled Nonlinear Electrical Transmission Lattice Using Sine-Cosine Method

This present work deals with the effect of fractional order (FO) on alphabetical shaped solitons solutions for intrinsic fractional (2+1)-D coupled nonlinear electrical transmission lattice using sine-cosine method in addition to the higher order of dispersion. We attained some exotical, alphabetical and new types of soliton solutions by performing the fractional nonlinear partial differential circuit equation including the fourth-order spatial dispersion -due to the semi-discrete approximation- with the simplest sine-cosine method. We derive the fractional nonlinear differential circuit equation by applying the Kirchhoff’s laws and aiding by the fractional complex transform in the modified Riemann-Liouville derivatives sense we establish a nonlinear ordinary differential equation. Thus, we carry out some novel FO’s effects. We even show that, the FO including the fourth-order spatial dispersion reveal the existence of M-shaped solitons, bi soliton-like in addition to the known effect like the amplitude’s increasing. We reach for the studied circuit that, the derived solutions by means of the sine-cosine method are functions of all the capacitor’s nonlinearities (quadratic and cubic) if and only if, we use the fourth-order spatial dispersion (FOSD) during the continuous media approximation. In contrast, in the absence of the FOSD term, the solutions only exist if, either the quadratic or the cubic nonlinearity is considered separately. Moreover, the fractional order also displays on the soliton’s width.