A Modified System of Nonlinear Fractional-Order Differential Equations in the Study of the Dynamics of Marital Relationships and their Behavioural Features

Abstract

Urbanization and modernization have effects on marital relationships in Nigeria which led to high divorce rate among legitimate couples prompting unstable environment. This situation design and uses scientific means to study the dynamics of marital relationships and their behavioural features to check excesses in marriage and to promote stability. A modified system of nonlinear fractional-order differential equations was used to categorize people of different personalities and different Impact Factors of Memory, using different sets of parameters. The equations predict and interpret the features of the union of different individuals with external circumstance(s). Equations were adapted to a local environment where data collections were carried out to investigate factors affecting marriages. Data collected by the use of questionnaire validate the model. An Iterative Decomposition Method was adopted to solve the fractional system in which fractional derivatives were given in the Caputo sense; the obtained results were interpreted appropriately. The modified model shows the trajectory of the couple from the state of indifference and as the impact factor memory increases it affects their togetherness making the love between them to decay easily. Numerical simulation results were presented to show the effectiveness of the model and the accuracy of the statements established. Keywords: Differential model, dynamical system, impact factors of memory, iterative decomposition method, marital relationship