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The study of the complex model associated with chaotic models is always the most complicated and fundamental in the current scientific environment. The primary goal of the current paper is to provide an illustration of the fundamental theory while analysing dynamical systems and validating the chaotic behaviour of the Lorenz–Haken (LH) equations, a system of fractional differential equations. The LH equations are used to describe the 4D chaotic laser. The Adams–Bashforth numerical method is used to extract the numerical solutions projected model. The classical model introduces the bifurcation of the parameter linked with the system. The system's uniqueness and existence are confirmed using the fixed-point hypothesis with the Caputo–Fabrizio fractional operator, followed by boundedness and dynamical analysis. Furthermore, the chaotic character of the numerical solutions with different orders obtained at different beginning circumstances is presented. [ABSTRACT FROM AUTHOR]