Solitary wave solutions for a time-fraction generalized Hirota–Satsuma coupled KdV equation by an analytical technique

• Published in: Applied mathematical modelling Vol. 33; no. 7; pp. 3107 - 3113
• Main Authors: Ganji, Z.Z., Ganji, D.D., Rostamiyan, Y.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Inc 01.07.2009; Elsevier
• Subjects: Caputo derivative; Exact sciences and technology; Fluid dynamics; Fractional generalized Hirota–Satsuma coupled KdV equations; Fundamental areas of phenomenology (including applications); General theory; Homotopy perturbation method; Physics; Fractional generalized Hirota–Satsuma coupled KdV equations; Caputo derivative; Homotopy perturbation method; Korteweg-de Vries equation; Solitary wave; coupled KdV equations; Fractional generalized Hirota-Satsuma; Homotopy; Perturbation techniques; Modelling; Non linear effect; Small parameter method; Fractional derivative
• ISSN: 0307-904X
• DOI: 10.1016/j.apm.2008.10.034

In this work, we implement a relatively analytical technique, the homotopy perturbation method (HPM), for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in Caputo derivatives. This method can be used as an alternative to obtain analytic and approximate solutions of different types of fractional differential equations which applied in engineering mathematics. The corresponding solutions of the integer order equations are found to follow as special cases of those of fractional order equations. He’s homotopy perturbation method (HPM) which does not need small parameter is implemented for solving the differential equations. It is predicted that HPM can be found widely applicable in engineering.