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Statistical and computational analysis for corruption and poverty model using Caputo-type fractional differential

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  • 1Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.

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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.

Keywords:
Euler's methodEviewsFixed point theoremFractional derivativeLinear model

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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.