<p>This paper examines the fractional Klein–Gordon–Zakharov system using the conformable fractional derivative, both quantitatively and qualitatively. Wielding the semi-inverse method (SIM) and travelling wave transformation (TWT), the variational principle is developed. Correspondingly, the Hamiltonian function is established based on the variational principle. Utilising the Galilean transformation, we derive the planar dynamical system, conduct a bifurcation analysis and discuss the existence of various wave solutions. In addition, the chaotic phenomenon is investigated by introducing an external perturbed term and the sensitivity analysis is presented in detail. Finally, two effective methods, namely the variational method that is based on the variational principle and the Ritz approach and the Hamiltonian-based method, are utilised to construct diverse wave solutions, including the bell-shaped solitary wave, anti-bell-shaped solitary wave, M-shaped wave (double bell-shaped solitary wave), W-shaped wave (double anti-bell-shaped solitary wave) and periodic wave solutions. The outlines of the obtained wave solutions are unfolded graphically and the impact of the fractional order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> on the extracted wave solutions is elaborated. As we all know, the findings of this exploration are new and have not been investigated before, which enables us to gain a deeper insight into the dynamics of the system under consideration.</p>