In this paper, the serial killing system is analyzed to construct a scheme for a fractional-order mathematical model having five compartments: \(S_h, W_h, C_h, G_h\) and \(J_h\) . The fractional-order serial killing model is investigated with the fractal fractional technique. For feasibility and mathematical study, we derive the results for boundedness with the Lipschitz condition, positivity, unique solution, and zone for a feasible solution by using Banach space and fixed point theory results. Furthermore, the continuity of the solution and Lyapunov’s first and second derivatives are used to verify the global stability of the proposed system. According to the equilibrium point, which supports the logical and experiential support of the proposed model, Solutions are derived using a Lagrange polynomial with two steps in the extended form of the Mittag Leffler kernel to analyze the influence of the fractional order and fractal dimension impact through simulations. Different effects of serial killing on the system are presented to specify the dynamical nature of the system, corresponding to different fractional derivatives and parameters. Simulations are derived for the proposed scheme to check the effectiveness of the results and to understand the effects of serial killing in society.
