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<p>Fractional mathematical model has been presented in this paper in order to describe the dynamics of a population’s perception of corruption, and how this is generated over time. To accomplish the objectives, it is necessary to explore the dynamics of the corruption model under fractional-order derivatives in the Caputo sense. This work is facilitated by stratifying the population into five compartments: susceptible, exposed, corrupts, recovered, and honest. A qualitative study of the problem is used to develop a unique solution by applying fixed-point theory to existing results. The generalized Adams-Bashforth Moulton method is used to solve the corruption model semi-analytically. Numerical simulations are conducted using Matlab for both integer and noninteger orders within the interval (0,&#xa0;1). Simulated results show that the model’s solution is stable and converges to a single point, regardless of the initial data. There is a significant improvement in stability outcomes with lower fractional orders. To complement the analysis of the considered model, we have applied the deep neural network method as well. We have taken two hidden layers for this network, the first is a tanh activation function, and the second is a linear activation function. Furthermore, the data set was divided into three categories: training, testing, and validation.</p>

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Exploring corruption dynamics through Caputo fractional models with deep neural network interventions

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Saira Tabassum,
  • Mati ur Rahman

摘要

Fractional mathematical model has been presented in this paper in order to describe the dynamics of a population’s perception of corruption, and how this is generated over time. To accomplish the objectives, it is necessary to explore the dynamics of the corruption model under fractional-order derivatives in the Caputo sense. This work is facilitated by stratifying the population into five compartments: susceptible, exposed, corrupts, recovered, and honest. A qualitative study of the problem is used to develop a unique solution by applying fixed-point theory to existing results. The generalized Adams-Bashforth Moulton method is used to solve the corruption model semi-analytically. Numerical simulations are conducted using Matlab for both integer and noninteger orders within the interval (0, 1). Simulated results show that the model’s solution is stable and converges to a single point, regardless of the initial data. There is a significant improvement in stability outcomes with lower fractional orders. To complement the analysis of the considered model, we have applied the deep neural network method as well. We have taken two hidden layers for this network, the first is a tanh activation function, and the second is a linear activation function. Furthermore, the data set was divided into three categories: training, testing, and validation.