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The improved fractional sub-equation method and its applications to the space-time fractional differential equations in fluid mechanics. (English) Zbl 1255.37022
Summary: By introducing a new general ansatz, the improved fractional sub-equation method is proposed to construct analytical solutions of nonlinear evolution equations involving Jumarie’s modified Riemann-Liouville derivative. By means of this method, the space-time fractional Whitham-Broer-Kaup and generalized Hirota-Satsuma coupled KdV equations are successfully solved. The obtained results show that the proposed method is quite effective, promising and convenient for solving nonlinear fractional differential equations.
MSC:
37L05General theory, nonlinear semigroups, evolution equations
35Q35PDEs in connection with fluid mechanics
35Q53KdV-like (Korteweg-de Vries) equations
35R11Fractional partial differential equations
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