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2 Journal of Applied Mathematics and Computational Mechanics

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Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences

Maitama Shehu, Zhao Weidong

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

71--82

Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He’s polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.

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.