Analytic solutions of the space–time conformable fractional Klein–Gordon equation in general form

Abstract

The Klein–Gordon equation plays an important role in mathematical physics. In this paper, a direct method which is very effective, simple, and convenient, is presented for solving the conformable fractional Klein–Gordon equation. Using this analytic method, the exact solutions of this equation are found in terms of the Jacobi elliptic functions. This method is applied to both time and space fractional equations. Some solutions are also illustrated by the graphics. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.