Deniz, Sinan2021-11-122021-11-122020-06-30https://doi.org/10.31801/cfsuasmas.450209http://hdl.handle.net/20.500.12575/76046In this paper, the Klein - Gordon equation is generalized using the concept of the variational order derivative. We try to construct the Crank-Nicholson scheme for numerical solutions of the modified Klein- Gordon equation. Stability analysis of the Crank-Nicholson scheme is examined and analyzed to prove the proposed method is stable for solving the time-fractional variable order Klein- Gordon equation. A numerical example is also given for illustration.enKlein-Gordon equationFractional variable order derivativeCrank-Nicholson schemeArticle6919819922618-6470