Abstract: We numerically solved a class of the KleinGordon equations with a nonlinear timefractional derivative of Caputo by using Jacobi spectral collocation method. First, the fractional KleinGordon equation was transformed into an integral differential equation with a singular kernel in the time by using the relation between the Caputo fractional derivative and the RiemannLiouville fractional integral, and then we used a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The results show that the numerical solution obtained by this method is a good approximation of the exact solution.

Key words: spectral collocation method, timefractional KleinCordon equation, Caputo fractional derivative