Merdan, Mehmet; Gökdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef

Purpose - In this article, the aim is to obtain an approximate analytical solution of time-fraction generalized Hirota-Satsuma coupled KDV with the help of the two dimensional differential transformation method (DTM). Exact solutions can also be obtained from the known forms of the series solutions. Design/methodology/approach - Two dimensional differential transformation method (DTM) is used. Findings - In this paper, the fractional differential transformation method is implemented to the solution of time-fraction generalized generalized Hirota-Satsuma coupled KDV with a number of initial and boundary values has been proved. DTM can be applied to many complicated linear and strongly nonlinear partial differential equations and does not require linearization, discretization, restrictive assumptions or perturbation. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. Originality/value - This is an original work in which the results indicate that the method is powerful and significant for solving time-fraction generalized generalized Hirota-Satsuma coupled KDV type differential equations.

Merdan, Mehmet; Yildirim, Ahmet; Gökdogan, Ahmet; Mohyud-Din, Syed Tauseef

In this article, homotopy perturbation method coupled with Laplace transform and Padé 0approximants is applied on the re-formulated nonlinear oscillatory systems. Numerical results and graphical represenations explicitly reveal the complete reliability and effeicincy of the suggested algorithm.

Merdan, Mehmet; Gökdogan, Ahmet; Yildirim, Ahmet; Mohyud-Din, Syed Tauseef

An approximate analytical solution of fractional Fornberg-Whitham equation was obtained with the help of the two-dimensional differential transformation method (DTM). It is indicated that the solutions obtained by the two-dimensional DTM are reliable and present an effective method for strongly nonlinear partial equations. Exact solutions can also be obtained from the known forms of the series solutions.