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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.

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 obtain approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions, by the homotopy analysis method (HAM).

The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

Approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions.

In this work, approximate analytical solution of the second order hyperbolic telegraph equation with initial conditions is obtained by the HAM. To show the efficiency of the present method, several examples are presented.

The purpose of this paper is to introduce a new version of the homotopy perturbation method (HPM) for solving the magnetohydrodynamic viscous flow due to a shrinking sheet.

Three terms from HPM solution are used.

The results show that this method is very effective and simple and can be applied to other nonlinear problems.

Comparison between the HPM and homotopy analysis methods for the studied problem shows a remarkable agreement and reveals that the HPM needs less work.

It is suggested that this method should be called HPM with auxiliary parameters. This paper uses two auxiliary parameters, three or more auxiliary parameters could be used for accuracy consideration.

In this paper, a two‐parameter HPM is applied which is useful for finding an approximate analytical solution of MHD viscous flow due to a shrinking sheet.

The nonlinear jerk equation is a third-order nonlinear equation that describes some physical phenomena and in general form is given by: x = J (x, x, x). The purpose of this paper is to employ the modified (MDTM) differential transform method (DTM) to obtain approximate periodic solutions of two cases of nonlinear jerk equation.

The approach is based on MDTM that is developed by combining DTM, Laplace transform and Padé approximant.

Comparison of results obtained by MDTM with those obtained by numerical solutions indicates the excellent accuracy of solution.

The MDTM is extended to determining approximate periodic solution of third-order nonlinear differential equations.

The purpose of this paper is to consider analytical solution of wave system in Rⁿ with coupling controllers by using the homotopy perturbation method (HPM).

HPM is applied to the system of linear partial differential equations, i.e. the system of waves in the two‐dimensional version of system equations (1) and (2). This problem is motivated by an analogous problem in ordinary differential equations for coupled oscillators and has potential application in isolating a vibrating object from the outside disturbances. For example, rubber or rubber‐like materials can be used to either absorb or shield a structure from vibration. As an approximation, these materials can be modeled as distributed springs.

In this paper, HPM was used to obtain analytical solution of wave system in with coupling controllers. The method provides the solutions in the form of a series with easily computable terms. Unlike other common methods for solving any physical problem, linear or nonlinear, that requires linearization, discretization, perturbation, or unjustified assumptions that may slightly change the physics of the problem, the HPM finds approximate analytical solutions by using the initial conditions only.

The method proposed in this paper is very reliable and efficient and is being used quite extensively for diversified nonlinear problems of a physical nature. The algorithm is being used for the first time on such problems.

The purpose of this work is to analytically examine the magnetohydrodynamic (MHD) Falkner‐Skan flow.

The series solution is obtained using the Adomian decomposition method (ADM) coupled with Padé approximants.

Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.

In this work, the MHD Falkner‐Skan flow is examined analytically. The series solution is obtained using the ADM coupled with Padé approximants. Comparison of the present solutions is made with the results obtained by other applied methods and excellent agreement is noted.

The purpose of this paper is to develop a scheme to study numerical solution of time fractional nonlinear evolution equations under initial conditions by reduced differential transform method.

The paper considers two models of special interest in physics with fractional‐time derivative of order, namely, the time fractional mKdV equation and time fractional convection diffusion equation with nonlinear source term.

The numerical results demonstrate the significant features, efficiency and reliability of the proposed method and the effects of different values are shown graphically.

The paper shows that the results obtained from the fractional analysis appear to be general.

The purpose of this paper is to obtain analytic solutions of telegraph equation by the homotopy Padé method.

The authors used Maple Package to calculate the solutions obtained from the homotopy Padé method.

The obtained approximation by using homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by [m, m] homotopy Padé technique are often independent of auxiliary parameter h and this technique accelerates the convergence of the related series. Finally, numerical results for some test problems with known solutions are presented and the numerical results are given to show the efficiency of the proposed techniques.

The paper is shown that homotopy Padé technique is a promising tool with accelerated convergence for complicated nonlinear differential equations.

The purpose of this paper is to report the effect of radiation on flow of a magneto‐micropolar fluid past a continuously moving plate with suction and blowing.

The governing equations are transformed into dimensionless nonlinear ordinary differential equations by similarity transformation. Analytical technique, namely the homotopy perturbation method (HPM) combining with Padé approximants and finite difference method, are used to solve dimensionless non‐linear ordinary differential equations. The skin friction coefficient and local Nusselt numbers are also calculated. Beside this, the comparison of the analytical solution with numerical solution is illustrated by the graphs for different values of dimensionless pertinent parameters.

The authors have studied laminar magneto‐micropolar flow in the presence of radiation by using HPM‐Padé and finite difference methods. Results obtained by HPM‐Padé are in excellent agreement with the results of numerical solution.

The HPM‐Padé is used in a direct way without using linearization, discritization or restrictive assumption. The authors have attempted to show the capabilities and wide‐range applications of the HPM‐Padé in comparison with the finite difference solution of magneto‐micropolar flow in the presence of radiation problem.