Solitary waves and modulation instability with the influence of fractional derivative order in nonlinear left-handed transmission line

The resolution of the reduced fractional nonlinear Schrödinger equation obtained from model describing wave propagation in left-handed transmission line presented by Djidere et al recently, allowed us this work through Adomian decomposition method (ADM) to highlight behavior and study process dark bright soliton solutions with effect derivative order as well Modulation Instability gain spectrum (MI) LHNLTL. By inserting derivatives sense Caputo structure approximate reduced, ADM is used. pipe order. bias MI instability zones occur when value tends 1. Furthermore, takes small values, stability appear. These results could bring new perspectives solitary waves metamaterials memory have a better future for modulated because paper stabilization solitons which be described values has been revealed. In addition, significant are find applications many research areas such field information communication technologies.