Deniz, S2024-07-182024-07-181303-5991http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/3597In 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. Numerical examples are also given for illustration.EnglishDIFFERENTIAL-EQUATIONSArticle