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Purpose -- The purpose of this paper is to apply the fractional sub-equation method to research on coupled fractional variant Boussinesq equation and fractional approximate long water wave equation. Design/methodology/approach -- The algorithm is implemented with the aid of fractional Ricatti equation and the symbol computational system Mathematica. Findings -- New travelling wave solutions, which include generalized hyperbolic function solutions, generalized trigonometric function solutions and rational solutions, for these two equations are obtained. Originality/value -- The algorithm is demonstrated to be direct and precise, and can be used for many other nonlinear fractional partial differential equations. The fractional derivatives described in this paper are in the Jumarie's modified Riemann-Liouville sense. [ABSTRACT FROM AUTHOR]