Numerical solution, conservation laws, and analytical solution for the 2D time-fractional chiral nonlinear Schrödinger equation in physical media

The (2+1)-dimensional time-fractional chiral non-linear Schr & ouml;dinger equation in physical media is considered in this paper. At the outset, the Lie group analysis is applied to build a set of infinitesimal generators for this equation with the aid of the Riemann-Liouville fractional derivatives. Consequently, the reduction for the considered equation into an ordinary differential equation of fractional order is obtained by using these generators and the ErdL & eacute;lyi-Kober fractional operator. As a result of this reduction, we use power series analysis to get an analytical solution provided by a convergence analysis of the obtained solution. Furthermore, we construct a numerical solution based on hyperbolic functions using the fractional reduced differential transform method in the sense of Caputo fractional derivatives. Also, we detect absolute errors by performing a comparison between the exact and numerical solutions of the equation under study, while investigating the effect of fractional order alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} on the numerical solution. Finally, conservation laws are derived using the the formal Lagrangian and new conservation theorem.