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**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.

### MSC:

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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\textit{H. H. Fadravi} et al., Int. J. Differ. Equ. 2011, Article ID 237045, 12 p. (2011; Zbl 1234.35298)

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### References:

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