Stability and numerical analysis of fractional BBM-Burger equation and fractional diffusion-wave equation with Caputo derivative

This paper gives a highly efficient technique to analyse the fractional BBM-Burger equation and fractional Diffusion-Wave equation. These equations are used to model various real-life phenomena like acoustic gravity waves, diffusion theory, anomalous diffusive systems, and wave propagation phenomena. A modified technique, which is the combination of the Homotopy perturbation method and Laplace transform, is used for getting the numerical solution. The Lyapunov function is used to investigate asymptotic stability, and the maximum absolute error for the proposed technique is also examined. The efficiency of the proposed technique is shown by computing the root mean square (RMS), L2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}^{2},$$\end{document} and L∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${L}^{\infty }$$\end{document} errors and comparing the results with the other techniques.