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Solving the fractional BBM-Burgers equation using the homotopy analysis method. (English) Zbl 1198.65205
Summary: Based on the homotopy analysis method, a scheme is developed to obtain approximation solution of a fractional BBM-Burgers equation with initial condition, which is introduced by replacing some integer-order space derivatives by fractional derivatives. The fractional derivatives are described in the Caputo sense. So the traditional homotopy analysis method for differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional differential equations. The solutions of our model equation are calculated in the form of convergent series with easily computable components.
Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:
 65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 35Q53 KdV equations (Korteweg-de Vries equations) 45K05 Integro-partial differential equations
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