The homotopy perturbation method applied to the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations. (English) Zbl 1219.35347

Gepreel, Khaled A.

Appl. Math. Lett. 24, No. 8, 1428-1434 (2011).

Summary: The fractional derivatives in the sense of Caputo, and the homotopy perturbation method are used to construct approximate solutions for nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equations with respect to time and space fractional derivatives. Also, we apply complex transformation to convert a time and space fractional nonlinear KPP equation to an ordinary differential equation and use the homotopy perturbation method to calculate the approximate solution. This method is efficient and powerful in solving wide classes of nonlinear evolution fractional order equations.

MSC:

35R11	Fractional partial differential equations
26A33	Fractional derivatives and integrals
35A35	Theoretical approximation in context of PDEs
35A22	Transform methods (e.g., integral transforms) applied to PDEs
35A24	Methods of ordinary differential equations applied to PDEs

Keywords:

homotopy perturbation method; fractional calculus; fractional Kolmogorov-Petrovskii-Piskunov equation; complex transformation

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