Modeling Divorce Dynamics Due to Extramarital Affairs with Piecewise Classical-Fractional Operator (Journal of Nonlinear Modeling and Analysis, 2025)
In recent decades, various methodologies have been proposed tomodel the complexities of challenging global problems across different domains.One such challenge involves understanding multi-step behaviors observed incertain situations. Newly proposed piecewise derivatives are known to address these issues. This study utilizes a mathematical model to examine thespread of a social issue of divorce among married couples resulting from extramarital affairs, using piecewise derivatives. Initially, we develop the modelwith Caputo fractional derivative and conduct some basic mathematical computations. Furthermore, the model is explored within the framework of thepiecewise operator, incorporating both classical and Caputo operators. Withinthis framework, the study presents the existence and uniqueness of the solutionusing the fixed-point results. To analyze the behavior of the considered model,the Newton polynomial interpolation method is employed. The findings aresubsequently illustrated through graphical representations, considering variousvalues of fractional order.