OICC Press Mathematical Sciences 2251-7456 15 4 (December 2021) 2021 01 16 New strategic method for fractional mitigating internet bottleneck with quadratic–cubic nonlinearity 10.1007/s40096-020-00373-2 EN Jalil Manafian Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IR Onur Alp Ilhan Department of Mathematics, Faculty of Education, Erciyes University, Melikgazi-Kayseri, 38039, TR Sherin Youns Mohyaldeen Business Administration Department, Zakho Technical Institute, Duhok Polytechnic University, Duhok, Kurdistan Region, IQ Subhiya M. Zeynalli Ganja State University, Ganja, AZ Gurpreet Singh Department of Mathematics, Sant Baba Bhag Singh University, Jalandhar, 144030, IN Journal Article 2021 01 16 Abstract In this article, the mitigating Internet bottleneck including quadratic–cubic nonlinearity containing the ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rho$$\end{document} -derivative has been considered that describes the control of Internet traffic. This equation is analyzed utilizing two integration schemes, videlicet, the extended sinh-Gordon equation expansion technique and improved tan(Ξ/2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tan (\Xi /2)$$\end{document} -expansion technique. Various kinds of traveling wave solutions by employing these schemes are presented: solitary, topological, periodic, kink-periodic, and soliton wave solutions. Moreover, the plenty of available solutions with guaranteed conditions are also presented. The restriction conditions for the existence of valid solutions are as well as listed. In order to shed more light on these novel solutions, graphical features 3D, 2D, and density with some suitable choice of parameter values have been depicted. The outcome indicates that the mitigating Internet bottleneck is used as an amplifying model in the applied sciences.