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 |