Bright and singular soliton solutions of the conformable time-fractional Klein–Gordon equations with different nonlinearities

Abstract

Finding the exact solutions of nonlinear fractional differential equations has gained considerable attention, during the past two decades. In this paper, the conformable time-fractional Klein–Gordon equations with quadratic and cubic nonlinearities are studied. Several exact soliton solutions, including the bright (non-topological) and singular soliton solutions are formally extracted by making use of the ansatz method. Results demonstrate that the method can efficiently handle the time-fractional Klein–Gordon equations with different nonlinearities. © 2017 Informa UK Limited, trading as Taylor & Francis Group.