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Statistical and computational analysis for corruption and poverty model using Caputo-type fractional differential
Mansour A Abdulwasaa1, Sunil V Kawale1, Mohammed S Abdo2,3
1Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.
Heliyon
|February 8, 2024
Summary
This study develops a mathematical model to understand poverty and corruption dynamics. It uses fractional calculus and nonlinear analysis to predict poverty rates and explore corruption control strategies.
Area of Science:
- Mathematical modeling
- Fractional calculus
- Nonlinear analysis
Background:
- Poverty and corruption are significantly correlated, necessitating research into control strategies.
- Mathematical approaches are being explored to model and understand the dynamics of poverty and corruption.
Purpose of the Study:
- To develop a mathematical model for the dynamics of poverty and corruption.
- To analyze indicators and predict poverty rates using linear and fractional models.
- To investigate optimal strategies for corruption control.
Main Methods:
- Linear model analysis with Eviews software.
- Formulation of a Caputo fractional derivative model.
- Nonlinear analysis for equilibrium points and basic reproduction number.
- Fixed point theory for existence and uniqueness of solutions.
- Modified Euler method for numerical analysis and Ulam-Hyers stability.
Main Results:
- Analysis of corruption and poverty indicators.
- Predictions of poverty rates for 2023-2024.
- Characterization of model properties like equilibrium points and reproduction number.
- Demonstration of solution existence, uniqueness, and stability.
- Graphical presentation of results and comparison with real data.
Conclusions:
- The study provides a robust mathematical framework for analyzing poverty and corruption dynamics.
- The developed fractional model offers insights into predicting poverty rates and informing corruption control strategies.
- Numerical simulations and stability analysis validate the model's applicability.
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