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The basic motivation of the present study is to extend the application of the local fractional Yang-Laplace decomposition method to solve nonlinear systems of local fractional partial differential equations. The differential operators are taken in the local fractional sense. The local fractional Yang-Laplace decomposition method (LFLDM) can be easily applied to many problems and is capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Two illustrative examples are given, revealing the effectiveness and convenience of the method.Keywords: Local fractional derivative operator, local fractional Yang-Laplace decomposition method, nonlinear systems of local fractional partial differential equations.

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In literature, there are many methods for solving nonlinear partial differential equations. In this paper, we develop a new method by combining Adomian decomposition method and Shehu transform method for solving nonlinear partial differential equations. This method can be named as Shehu transform decomposition method (STDM). Some examples are solved to show that the STDM is easy to apply.

The basic motivation of the present study is to apply the local fractional Sumudu decomposition method to solve linear system of local fractional partial differential equations. The local fractional Sumudu decomposition methodl (LFSDM) can easily be applied to many problems and it's capable of reducing the size of computational work to find non-differentiable solutions for similar problems. Some illustrative examples are given, revealing the effectiveness and convenience of this method. KeywordsLocal fractional derivative operator, local fractional Sumudu decomposition method, linear systems of local fractional partial differential equations.

The idea proposed in this work is to extend the Aboodh transform method to resolve the nonlinear partial differential equations by combining them with the so-called homotopy analysis method (HAM). This method can be called homotopy analysis aboodh transform method (HAATM). The results obtained by the application to the proposed examples show that this method is easy to apply and can therefore be used to solve other nonlinear partial differential equations.

The idea, which will be communicated through this paper is to make a change to the proposed method by Tarig M. Elzaki [21] and we extend it to solve nonlinear partial differential equations with time-fractional derivative. This document also includes illustrative examples show us how to apply this method, we also show the interest of combining these two methods is the speed of the calculates the terms, and not calculating the Lagrange multipliers.

In this paper, the fractional homotopy perturbation transform method (FHPTM) is employed to obtain approximate analytical solutions of the time-fractional KdV, K(2,2) and Burgers equations. The FHPTM can easily be applied to many problems and is capable of reducing the size of computational work. The fractional derivative is described in the Caputo sense. The results show that the FHPTM is an appropriate method for solving nonlinear fractional derivative equation.