Jarad, FahdAl-Qurashi, MaysaaSultana, SobiaKarim, ShaziaRashid, SaimaJarad, FahdAlharthi, Mohammed Shaaf2023-12-292023-12-292023Al-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,24736988https://hdl.handle.net/20.500.12416/6825Divorce 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 R¯0 . The existence and stability of the equilibrium point can be assessed using ¯R0, 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/openAccessCounselingDivorce Epidemic ModelFractal-Fractional Atangana-Baleanu Derivative OperatorNumerical SolutionsStability AnalysisArticle835233526510.3934/math.2023263