Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling

Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity $ \bar{\mathbb{R}_{0}} $. The existence and stability of the equilibrium point can be assessed using $ \bar{\mathbb{R}}_0 $, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.