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A coupling method of homotopy perturbation and Laplace transformation for fractional models. (English) Zbl 1245.65143

Summary: This paper suggests a novel coupling method of homotopy perturbation and Laplace transformation for fractional models. This method is based on He’s homotopy perturbation, Laplace transformation and the modified Riemann-Liouville derivative. However, all the previous works avoid the term of fractional order initial conditions and handle them as a restricted variation. In order to overcome this shortcoming, a fractional Laplace homotopy perturbation transform method (FLHPTM) is proposed with modified Riemann-Liouville derivative. The results from introducing a modified Riemann-Liouville derivative, fractional order initial conditions and Laplace transform in the cases studied show the high accuracy, simplicity and efficiency of the approach.

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
44A10 Laplace transform
26A33 Fractional derivatives and integrals
35R11 Fractional partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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