@Article{cmc.2010.015.221, AUTHOR = {Chein-Shan Liu}, TITLE = {The Fictitious Time Integration Method to Solve the Space- and Time-Fractional Burgers Equations}, JOURNAL = {Computers, Materials \& Continua}, VOLUME = {15}, YEAR = {2010}, NUMBER = {3}, PAGES = {221--240}, URL = {http://www.techscience.com/cmc/v15n3/22538}, ISSN = {1546-2226}, ABSTRACT = {We propose a simple numerical scheme for solving the space- and time-fractional derivative Burgers equations: Dtαu + εuux = vuxx + ηDxβu, 0 < α, β ≤ 1, and ut + D*β(D*1-βu)2/2 = vuxx, 0 < β ≤ 1. The time-fractional derivative Dtαu and space-fractional derivative Dxβu are defined in the Caputo sense, while D*βu is the Riemann-Liouville space-fractional derivative. A fictitious time τ is used to transform the dependent variable u(x,t) into a new one by (1+τ)γu(x,t) =: v(x,t,τ), where 0 < γ ≤ 1 is a parameter, such that the original equation is written as a new functional-differential type partial differential equation in the space of (x,t,τ). When the group-preserving scheme is used to integrate these equations under a semi-discretization of u(x,t,τ) at the spatial-temporal grid points, we can achieve rather accurate solutions.}, DOI = {10.3970/cmc.2010.015.221} }