On the comparative study for Klein–Fock–Gordon equation: Fractional exact solutions, bifurcation and sensitivity analysis

Abstract

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.