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A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Khalouta Ali, Kadem Abdelouahab

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

45--58

The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.

On Analytical Approximate Solution of the Fractional Type Rosenau-Hyman Equation

Babaei A.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

135--143

In this paper, an approximate solution of the fractional type Rosenau-Hyman equation according to an appropriate initial condition will be obtained with the help of the reduced differential transform method (RDTM). The fractional derivatives are described in the Caputo sense. Comparing the methodology with the homotopy perturbation method and the variational iteration method will be presented. The results show that solutions obtained by the RDTM are reliable and this method is effective for this type of nonlinear fractional partial differential equations.