Chein-Shan Liu1
CMC-Computers, Materials & Continua, Vol.15, No.3, pp. 221-240, 2010, DOI:10.3970/cmc.2010.015.221
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… More >
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