Application of homotopy analysis method for solving nonlinear fractional partial differential equations
Keywords:
Analytical solution, Nonlinear fractional heat conduction, Kaup-Kupershmidt, Fisher, Huxley, Burgers–Fisher and Burgers–Huxley equations, Fractional partial differential equations (FPDEs), Homotopy analysis methodAbstract
In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations.Based on the homotopy analysis method, a scheme is developed to obtain the approximate solution of the nonlinearfractional heat conduction, Kaup–Kupershmidt, Fisher and Huxley equations with initial conditions, introduced byreplacing some integer-order time derivatives by fractional derivatives. The solutions of the studied models are calculatedin the form of convergent series with easily computable components. The results of applying this procedure tothe studied cases show the high accuracy and efficiency of the new technique. The fractional derivative is describedin the Caputo sense. Some illustrative examples are presented to observe some computational results.References
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