Fourier Spectral Method for Nonlinear Time-Fractional Sine-Gordon Equations

In this paper, the nonlinear time-fractional Sine-Gordon equation is investigated via the Fourier spectral method. The time-fractional derivative is approximated by the L1 approximation scheme, and the spatial component is discretized using the Fourier spectral method. The existence and uniqueness of the numerical solution are proven, and the stability and convergence of the proposed method are analyzed, respectively. Theoretical results are validated by numerical experiment.