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

Mansour A Abdulwasaa; Sunil V Kawale; Mohammed S Abdo; M Daher Albalwi; Kamal Shah; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.1016/j.heliyon.2024.e25440

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

Heliyon. 2024 Feb 1;10(3):e25440. doi: 10.1016/j.heliyon.2024.e25440. eCollection 2024 Feb 15.

Authors

Mansour A Abdulwasaa¹, Sunil V Kawale¹, Mohammed S Abdo^{2

3}, M Daher Albalwi⁴, Kamal Shah^{3

5

6}, Bahaaeldin Abdalla³, Thabet Abdeljawad^{3

7

8}

Affiliations

¹ Department of Statistics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, India.
² Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen.
³ Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.
⁴ Yanbu Industrial College, The Royal Commission for Jubail and Yanbu, 30436, Saudi Arabia.
⁵ Department of Mathematics, University of Malakand, Chakdara, Dir(L) 18000, KPK, Pakistan.
⁶ Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon.
⁷ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
⁸ Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa.

Abstract

Since there is a clear correlation between poverty and corruption, mathematicians have been actively researching the concept of poverty and corruption in order to develop the optimal strategy of corruption control. This work aims to develop a mathematical model for the dynamics of poverty and corruption. First, we study and analyze the indicators of corruption and poverty rates by applying the linear model along with the Eviews program during the study period. Then, we present a prediction of poverty rates for 2023 and 2024 using the results of the standard problem-free model. Next, we formulate the model in the frame of Caputo fractional derivatives. Fundamental properties, including equilibrium points, basic reproduction number, and positive solutions of the considered model are obtained using nonlinear analysis. Sufficient conditions for the existence and uniqueness of solutions are studied via using fixed point theory. Numerical analysis is performed by using modified Euler method. Moreover, results about Ulam-Hyers stability are also presented. The aforementioned results are presented graphically. In addition, a comparison with real data and simulated results is also given. Finally, we conclude the work by providing a brief conclusion.

Keywords: Euler's method; Eviews; Fixed point theorem; Fractional derivative; Linear model.