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Analysis of nonlinear fractional partial differential equations with the homotopy analysis method. (English) Zbl 1221.65286
Summary: The time fractional partial differential equations are investigated by means of the homotopy analysis method. This technique is extended to study the partial differential equations of fractal order for the first time. The accurate series solutions are obtained. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional partial differential equations.
MSC:
65M99Numerical methods for IVP of PDE
35K20Second order parabolic equations, initial boundary value problems
35R11Fractional partial differential equations