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