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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.

Two dimensional differential transformation method (DTM) is used.

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.

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.

The purpose of this paper is to show how an application of fractional two dimensional differential transformation method (DTM) obtained approximate analytical solution of time‐fraction modified equal width wave (MEW) equation.

The fractional derivative is described in the Caputo sense.

It is indicated that the solutions obtained by the two dimensional DTM are reliable and that this is an effective method for strongly nonlinear partial equations.

The paper shows that exact solutions can also be obtained from the known forms of the series solutions.

The main purpose of the work is to demonstrate the eligibility of the methods applied and to have the more reliable and user friendly approaches to find the solution of the applicable governing equations such as of the MHD flow.

The numerical and semi analytical methods have been applied to solve the governing equations. The reliability of the methods is also approved by a comparison made between the results obtained and the results of the former studies performed using the other numerical approach.

The reliability of the methods are approved, so that the method could be used to discuss more in depth arguments on the different profiles of the solution.

It could be considered as a first endeavor to use the solution of the MHD Jeffery Hamel flow using this kind of numerical method along with the semi analytical approach.