On the solutions of nonlinear fractional Klein–Gordon equation with modified Riemann–Liouville derivative

In this paper, fractional variational iteration method (FVIM) is applied for finding approximate analytical solutions of nonlinear fractional Klein–Gordon equation. Time-fractional derivative is described in the Riemann–Liouville sense. A new application of fractional variational iteration method (FVIM) is extended to derive analytical solutions in the form of a series for this equation. The behavior of the solutions and the effects of different values of fractional order αα are indicated graphically. It is shown that the solutions obtained by the FVIM are reliable, convenient and effective for strongly nonlinear partial equations with modified Riemann–Liouville derivative.