A COUPLING METHOD OF HOMOTOPY PERTURBATION AND LAPLACE TRANSFORMATION FOR FRACTIONAL MODELS

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.