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The purpose of this paper is to apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation, which plays a very important role in mathematical physics and engineering sciences.

The authors apply exp‐function method to construct generalized solitary and periodic solutions of Fitzhugh‐Nagumo equation.

Numerical results clearly indicate the reliability and efficiency of the proposed exp‐function method. The suggested algorithm is quite efficient and is practically well suited for use in these problems.

In this paper, the authors applied the exp‐function method to obtain solutions of the Fitzhugh‐Nagumo equation and show that the exp‐function method gives more realistic solutions without disturbing the basic physics of the physical problems.

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 simulate nanofluid laminar steady flow in a lid-driven porous cavity under the impact of Lorentz forces.

Shape effect of nanoparticles and magnetic field impact on nanofluid properties are taken into consideration. The solutions of final equations are obtained by control volume based finite element method (CVFEM).

Graphs are depicted for different values of Darcy number, Fe₃O₄-water volume fraction, Reynolds and Hartmann numbers.

Results illustrated that using Platelet-shaped nanoparticles results in the highest Nusselt number. Nusselt number augments with rise of Darcy and Reynolds number.