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Homotopy perturbation method for fractional KdV-Burgers equation. (English) Zbl 1132.65118

Summary: We extend the homotopy perturbation method to solve nonlinear fractional partial differential equations. The time- and space-fractional Korteweg-de Vries (KdV)-Burgers equations with initial conditions are chosen to illustrate our method. As a result, we successfully obtain some available approximate solutions of them. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of nonlinear fractional partial differential equations.

MSC:

65R20 Numerical methods for integral equations
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
45K05 Integro-partial differential equations
45G10 Other nonlinear integral equations
26A33 Fractional derivatives and integrals
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