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A new numerical technique for solving fractional Bratu’s initial value problems in the Caputo and Caputo-Fabrizio sense

Khalouta Ali, Kadem Abdelouahab

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 1

43--56

The purpose of this paper is to propose a new numerical technique called the natural decomposition method (NDM) for solving fractional Bratu’s initial value problems (FBIVP) in the Caputo and Caputo-Fabrizio sense. The NDM is a combined form of the natural transform method and the Adomian decomposition method. The numerical example is provided in order to validate the efficiency and reliability of the proposed method. The obtained results reveal that the proposed method is a very efficient and simple tool for solving fractional differential equations.

The Generalized Differential Transform Method for solution of a free vibration linear differential equation with fractional derivative damping

Das Deepanjan

Journal of Applied Mathematics and Computational Mechanics

2019

Vol. 18, nr 2

19--29

In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.