A unified approach for the numerical solution of time fractional Burgers’ type equations

In this paper, a relatively new approach is devised for obtaining approximate solution of time fractional partial differential equations. Time fractional diffusion equation and time fractional Burgers-Fisher equation are solved with Haar wavelet method where fractional derivatives are Caputo derivative. Time discretization of the problems made by L1 discretization formula and space derivatives discretized by Haar series. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{2}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ L_{\infty}$\end{document} error norms are used for measuring accuracy of the proposed method. Numerical results obtained with proposed method compared with exact solutions as well as with available results from the literature. The numerical results verify the feasibility of Haar wavelet combined with L1 discretization formula for the considered problems.