Modified Kudryashov method for solving the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities

The nonlinear time-fractional Klein-Gordon equations play an important role in describing some physical events in solid state physics, nonlinear optics, and quantum field theory. In this paper, the time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities in the sense of the conformable fractional derivative are solved via the modified Kudryashov method. A few new explicit exact solutions of these equations are formally constructed. Results confirm the efficiency of the modified Kudryashov method in handling the conformable time-fractional Klein-Gordon equations with quadratic and cubic nonlinearities.