Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

Abstract

This study investigates the exact solutions of the time-fractional (3+1)-dimensional combined Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM) equation. The considered model describes the long surface gravity waves of small amplitude, which portrays the two-way propagation of waves. The modified generalized Kudryashov method and the exp(-φ(ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi (\\xi $$\\end{document}))-expansion methods are employed to resolve the aforementioned issue because of their effectiveness and simplicity. For generality, the time fractional version is studied; more advanced solutions that do not exist in the literature were obtained. As a result, a variety of the exact wave solutions of the conformable (3+1)-dimensional KdV-BBM equation are obtained. The dynamical behaviors of some obtained solutions are represented with the proper parameter values. The used methods yield noteworthy results in obtaining the analytical solutions of fractional differential equations under various conditions. Besides, the sensitivity of regarding dynamical system is assessed to show the numerical stability effects.