Homotopy analysis method for solving foam drainage equation with space- and time-fractional derivatives. (English) Zbl 1234.35298

Summary: The analytical solution of the foam drainage equation with time- and space-fractional derivatives was derived by means of the homotopy analysis method (HAM). The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made; the comparisons show that the homotopy analysis method is very effective and convenient. By choosing different values of the parameters \(\alpha, \beta\) in general formal numerical solutions, as a result, a very rapidly convergent series solution is obtained.


35R11 Fractional partial differential equations
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
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