A new efficient method for time-fractional Sine-Gordon equation with the Caputo and Caputo-Fabrizio operators

Ali Khalouta\(^1\)
Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif University 1, 19000 Setif, Algeria.
Abdelouahab Kadem
Laboratory of Fundamental and Numerical Mathematics, Department of Mathematics, Faculty of Sciences, Ferhat Abbas Setif University 1, 19000 Setif, Algeria.
\(^{1}\)Corresponding Author: nadjibkh@yahoo.fr

Copyright © 2020 Ali Khalouta, Abdelouahab Kadem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2020

Abstract

In this work, a new efficient method called, Elzaki’s fractional decomposition method (EFDM) has been used to give an approximate series solutions to time-fractional Sine-Gordon equation. The time-fractional derivatives are described in the Caputo and Caputo-Fabrizio sense. The EFDM is based on the combination of two different methods which are: the Elzaki transform method and the Adomian decomposition method. To demonstrate the accuracy and efficiency of the proposed method, a numerical example is provided. The obtained results indicate that the EFDM is simple and practical for solving the fractional partial differential equations which appear in various fields of applied sciences.

Keywords:

time-fractional Sine-Gordon equation, Caputo fractional derivative operator, Caputo-Fabrizio fractional derivative operator, Elzaki transform, Adomian decomposition method, approximate series solution.