Al-Qurashi, MaysaaJarad, FahdSultana, SobiaKarim, ShaziaRashid, SaimaJarad, FahdAlharthi, Mohammed ShaafMatematik2023-12-292023-12-292023Al-Qurashi, Maysaa;...ET.AL. (2023). "Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling", AIMS Mathematics,2473-6988https://doi.org/10.3934/math.2023263Divorce 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 over bar R0. The existence and stability of the equilibrium point can be assessed using R over bar 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.eninfo:eu-repo/semantics/openAccessDivorce Epidemic ModelFractal-Fractional Atangana-Baleanu Derivative OperatorNumerical SolutionsCounselingStability AnalysisArticle835233526510.3934/math.20232632-s2.0-85144050717WOS:000913206300006Q1Q1