Khan, Yasir; Faraz, Naeem; Kumar, Sunil; Yildirim, Ahmet A coupling method of homotopy perturbation and Laplace transformation for fractional models. (English) Zbl 1245.65143 Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 74, No. 1, 57-68 (2012). 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. Cited in 11 Documents 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 Keywords:Laplace transform; modified Riemann-Liouville derivative; homotopy perturbation method; initial value problem; fractional models PDFBibTeX XMLCite \textit{Y. Khan} et al., Sci. Bull., Ser. A, Appl. Math. Phys., Politeh. Univ. Buchar. 74, No. 1, 57--68 (2012; Zbl 1245.65143)