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

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.