A modified system of nonlinear fractional-order differential equations become used to classify humans of various personalities and different Impact Factors of Memory (IFM); with unique set of model parameters. The model was used to interpret and predict the functions of the union of various people with external circumstance(s) and adapted to neighborhood environment in which the statistics collections were achieved to analyze numerous measures affecting marriages, unique challenges in marriage and associated occasions were investigated through the use of questionnaire. Data had been analyzed and the outcomes have been carried out as parameters to validate the model. Adams Predictor-Corrector Method was used to test the chaoticity of the system and it was confirmed via numerical simulations. Numerical simulation outcomes had been presented to reveal the effectiveness of the model and the accuracy of the statements established. The mathematical information implied by the model unveil an underlying mechanism which can give an explanation for couple disruption in relationships that were initially deliberated to remain all the time. Despite the terrible aspects of relationships, some human beings were still satisfied in their intimate members of the family. The study was addressed on a field survey (use of questionnaires) and with the aid of interrogating the members one on one. A feasible path for future work is the choice to attain balance through modelling and to validate the results with the aid of numerical simulations.
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
In this research article, an Iterative Decomposition Method is applied to approximate linear and non-linear fractional delay differential equation. The method was used to express the solution of a Fractional delay differential equation in the form of a convergent series of infinite terms which can be effortlessly computable.The method requires neither discretization nor linearization. Solutions obtained for some test problems using the proposed method were compared with those obtained from some methods and the exact solutions. The outcomes showed the proposed approach is more efficient and correct.
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