A variety of solitary waves solutions for the modified nonlinear Schrödinger equation with conformable fractional derivative

This study aims to examine the conformable time-fractional modified nonlinear Schrödinger equation, by employing two exact techniques. The governing model namely, modified nonlinear Schrödinger equation have many application in the field of ocean engineering. The two variables G′G,1G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( \frac{G'}{G},\frac{1}{G}\right) $$\end{document}-expansion method and the generalized projective Riccati equations method are utilized to determine a spectrum of optical solitary wave solutions with different values of conformable fractional parameters. The obtained exact solutions include singular, dark and bright solitons. The graphical depiction of 3D plots and corresponding line plots of different acquired solutions have been given for suitable parametric conditions. The dynamical behavior of governing model is determined by imposing constraint conditions. The graphical observations show the conformable fractional operator provides continuously evolving wave form for both utilized integration techniques and hence may be useful to study more fractional order models.