Computational modeling of financial crime population dynamics under different fractional operators
This paper presents an analysis and numerical simulation of financial crime population dynamics using fractional order calculus and Newton's polynomial. The dynamics of financial crimes are modeled as a fractional-order system, which is then solved using numerical methods based on Newton's...
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AIMS Press
2023-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231058?viewType=HTML |
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| author | Rahat Zarin Abdur Raouf Amir Khan Aeshah A. Raezah Usa Wannasingha Humphries |
| author_facet | Rahat Zarin Abdur Raouf Amir Khan Aeshah A. Raezah Usa Wannasingha Humphries |
| author_sort | Rahat Zarin |
| collection | DOAJ |
| description | This paper presents an analysis and numerical simulation of financial crime population dynamics using fractional order calculus and Newton's polynomial. The dynamics of financial crimes are modeled as a fractional-order system, which is then solved using numerical methods based on Newton's polynomial. The results of the simulation provide insights into the behavior of financial crime populations over time, including the stability and convergence of the systems. The study provides a new approach to understanding financial crime populations and has potential applications in developing effective strategies for combating financial crimes. Fractional derivatives are commonly applied in many interdisciplinary fields of science because of its effectiveness in understanding and analyzing complicated phenomena. In this work, a mathematical model for the population dynamics of financial crime with fractional derivatives is reformulated and analyzed. A fractional-order financial crime model using the new Atangana-Baleanu-Caputo (ABC) derivative is introduced. The reproduction number for financial crime is calculated. In addition, the relative significance of model parameters is also determined by sensitivity analysis. The existence and uniqueness of the solution in consideration of the ABC derivative are discussed. A number of conditions are established for the existence and Ulam-Hyers stability of financial crime equilibria. A numerical scheme is presented for the proposed model, starting with the Caputo-Fabrizio fractional derivative, followed by the Caputo and Atangana-Baleanu fractional derivatives. Finally, we solve the models with fractal-fractional derivatives. |
| first_indexed | 2024-03-13T00:36:26Z |
| format | Article |
| id | doaj.art-0b0f4cce2b3848d486dfc84d1c68b347 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-13T00:36:26Z |
| publishDate | 2023-06-01 |
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| series | AIMS Mathematics |
| spelling | doaj.art-0b0f4cce2b3848d486dfc84d1c68b3472023-07-10T01:32:18ZengAIMS PressAIMS Mathematics2473-69882023-06-0189207552078910.3934/math.20231058Computational modeling of financial crime population dynamics under different fractional operatorsRahat Zarin0Abdur Raouf 1Amir Khan2Aeshah A. Raezah3Usa Wannasingha Humphries41. Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand2. Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan2. Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan3. Department of Mathematics, Faculty of Science, Abha 62529, King Khalid University, Saudi Arabia1. Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandThis paper presents an analysis and numerical simulation of financial crime population dynamics using fractional order calculus and Newton's polynomial. The dynamics of financial crimes are modeled as a fractional-order system, which is then solved using numerical methods based on Newton's polynomial. The results of the simulation provide insights into the behavior of financial crime populations over time, including the stability and convergence of the systems. The study provides a new approach to understanding financial crime populations and has potential applications in developing effective strategies for combating financial crimes. Fractional derivatives are commonly applied in many interdisciplinary fields of science because of its effectiveness in understanding and analyzing complicated phenomena. In this work, a mathematical model for the population dynamics of financial crime with fractional derivatives is reformulated and analyzed. A fractional-order financial crime model using the new Atangana-Baleanu-Caputo (ABC) derivative is introduced. The reproduction number for financial crime is calculated. In addition, the relative significance of model parameters is also determined by sensitivity analysis. The existence and uniqueness of the solution in consideration of the ABC derivative are discussed. A number of conditions are established for the existence and Ulam-Hyers stability of financial crime equilibria. A numerical scheme is presented for the proposed model, starting with the Caputo-Fabrizio fractional derivative, followed by the Caputo and Atangana-Baleanu fractional derivatives. Finally, we solve the models with fractal-fractional derivatives.https://www.aimspress.com/article/doi/10.3934/math.20231058?viewType=HTMLfinancial crimestabilityreproduction numberfractional modelingnumerical schemes |
| spellingShingle | Rahat Zarin Abdur Raouf Amir Khan Aeshah A. Raezah Usa Wannasingha Humphries Computational modeling of financial crime population dynamics under different fractional operators AIMS Mathematics financial crime stability reproduction number fractional modeling numerical schemes |
| title | Computational modeling of financial crime population dynamics under different fractional operators |
| title_full | Computational modeling of financial crime population dynamics under different fractional operators |
| title_fullStr | Computational modeling of financial crime population dynamics under different fractional operators |
| title_full_unstemmed | Computational modeling of financial crime population dynamics under different fractional operators |
| title_short | Computational modeling of financial crime population dynamics under different fractional operators |
| title_sort | computational modeling of financial crime population dynamics under different fractional operators |
| topic | financial crime stability reproduction number fractional modeling numerical schemes |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231058?viewType=HTML |
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