CHINESE JOURNAL OF PHYSICS, vol.89, pp.453-468, 2024 (SCI-Expanded)
In this study, we consider the Klein–Fock–Gordon equation model that emerges in the fields
of quantum field theory, condensed matter physics and theory of relativity etc. The exact
solutions of the model with various physical properties were systematically created in terms of
Beta, Atangana–Baleanu meaning Caputo and M-fractional fractional derivatives. 3-D graphic
analysis, physical interpretations of solutions and comparisons of derivative operators are
presented. The fact that the solutions to be presented are different from those in the literature
and examining the effects of different fractional derivative operators on the solutions are among
the novelties of the study. In the last part of the article, bifurcation analysis and sensitivity
analysis were performed and phase portraits shown. At the same time we examine the effects
of some parameters on sensitivity.