Exact solitary optical wave solutions and modulational instability of the truncated Ω-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega -$$\end{document}fractional Lakshamanan–Porsezian–Daniel model with Kerr, parabolic, and anti-cubic nonlinear laws

In this article we have acquired exact solitary wave solutions for the truncated Ω-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega -$$\end{document}fractional Lakshamanan–Porsezian–Daniel model with Kerr, parabolic, and anti-cubic nonlinear laws employing extended auxiliary technique. Diverse set of exponential function solutions acquired relying on a map between the considered equation and an auxiliary ODE. Obtained solutions are recast in several hyperbolic and trigonometric forms based on different restrictions between parameters involved in equations and integration constants that appear in the solution. A few significant ones among the reported solutions are pictured to perceive the physical utility and peculiarity of the considered model using mathematical software. In the end, the modulation instability analysis of the proposed model with normal derivatives is also carried out for Kerr, parabolic, and anti-cubic nonlinear laws. For these three cases, dispersion relations are obtained and explained with plots. Results turned out here may be useful in network technology to study the characteristics of fiber optic communication over inter-continental distances.