A numerical investigation of marriage divorce model: Fractal fractional perspective

Abstract

Even if a marriage began as “till forever”, divorce is a legal way for married couples to end their relationship. Divorce, indeed, is a complex process that may be seen from several perspectives. Sociologists believe that the family gives more than simply individuals. It is the structure that allows individuals to develop mentally while also providing the necessary educational and financial assistance. Divorced spouses face economic, social, and financial exploitation. This, in turn, disintegrates families and diminishes the concept of the family as the core unit of society, causing society to become stalled. The breakup of families that will produce healthy and happy children in the future is a significant societal issue. According to Eurostat statistics, the number of crude marriages in European nations was 8 in 1964 and 4.3 in 2014. At the same period, crude divorce rates grew by more than twice as much, from 0.8 in 1964 to 1.8 in 2019. In 2022, Latvia, Lithuania, and Denmark had the most number of divorces. Considering the datas, the investigation of this phenomenon, which deeply injures and shakes society, by various branches of science and the study of its dynamics has become an important objective and mathematical analysis of divorce illuminates the motivation for this paper. Therefore, the mathematical model of divorce is considered with by the fractal fractional Caputo–Fabrizio derivative. Firstly, using Equilibrium points, the model’s linear stability is obtained. Then, the existence and uniqueness the solution of the model was proven by the Banach Fixed point theorem. Lastly, the behavior of the model is evaluated using graphics for different values of the fractal dimension and fractional derivative by developing a numerical method for the model that contains the fractal fractional derivative. Experimental results are analyzed for different instances of the key parameters that played major roles for each of the sub-population classes.