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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.
65M99Numerical methods for IVP of PDE
44A10Laplace transform
26A33Fractional derivatives and integrals (real functions)
35R11Fractional partial differential equations
35A22Transform methods (PDE)