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Research Article

Exploring the role of fractal-fractional operators in mathematical modelling of corruption

, , , , &
Article: 2233678 | Received 26 Apr 2023, Accepted 27 Jun 2023, Published online: 12 Jul 2023

References

  • Kaufmann D. Myths and realities of governance and corruption. Available at SSRN 829244. 2005.
  • Kaufmann D, Vicente PC. Legal corruption. Econ Politics. 2011;23(2):195–219. doi: 10.1111/ecpo.2011.23.issue-2
  • Lehtinen J, Locatelli G, Sainati T, et al. The grand challenge: effective anti-corruption measures in projects. Int J Proj Manag. 2022;40(4):347–361. doi: 10.1016/j.ijproman.2022.04.003
  • Gibbon E. History of the decline and fall of the roman empire† volume 1. New York: Prabhat Prakashan; 2021.
  • Abdulrahman S. Stability analysis of the transmission dynamics and control of corruption. Pac J Sci Technol. 2014;15(1):99–113. https://www.akamai.university/files/theme/AkamaiJournal/PJST15_1_99.pdf
  • Brianzoni S, Coppier R, Michetti E. Complex dynamics in a growth model with corruption in public procurement. Discrete Dynamics in Nature and Society 2011. 2011..
  • Khan MAU. The corruption prevention model. J Discret Math Sci Cryptogr. 2000;3(1-3):173–178. doi: 10.1080/09720529.2000.10697905
  • Cuervo-Cazurra A. Corruption in international business. J World Bus. 2016;51(1):35–49. doi: 10.1016/j.jwb.2015.08.015
  • Athithan S, Ghosh M, Li X-Z. Mathematical modeling and optimal control of corruption dynamics. Asian-Eur J Math. 2018;11(06):1850090. doi: 10.1142/S1793557118500900
  • Lemecha L. Modelling corruption dynamics and its analysis. Ethiop J Sci Sustain Dev. 2018;5(2):13–27. doi: 10.20372/ejssdastu:v5.i2.2018.34
  • Jose SA, Raja R, Alzabut J, et al. Mathematical modeling on transmission and optimal control strategies of corruption dynamics. Nonlinear Dyn. 2022;109(4):3169–3187. doi: 10.1007/s11071-022-07581-6
  • Shah K, Abdalla B, Abdeljawad T, et al. Analysis of multipoint impulsive problem of fractional-order differential equations. Bound Value Probl. 2023;2023(1):1–17. doi: 10.1186/s13661-022-01688-w
  • Owolabi KM, Pindza E. A nonlinear epidemic model for tuberculosis with Caputo operator and fixed point theory. Healthcare Anal. 2022;2:100111. doi: 10.1016/j.health.2022.100111
  • Eskandari Z, Avazzadeh Z, Khoshsiar Ghaziani R, et al. Dynamics and bifurcations of a discrete-time Lotka–Volterra model using nonstandard finite difference discretization method. Mathematical Methods in the Applied Sciences. 2022.
  • Jin F, Qian Z-S, Chu Y-M, et al. On nonlinear evolution model for drinking behavior under Caputo-Fabrizio derivative. J Appl Anal Comput. 2022;12(2):790–806. doi: 10.11948/20210357
  • Doungmo Goufo EF. Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: basic theory and applications. Chaos Interdiscip J Nonlinear Sci. 2016;26(8):084305. doi: 10.1063/1.4958921
  • Sinan M, Ansari KJ, Kanwal A, et al. Analysis of the mathematical model of cutaneous Leishmaniasis disease. Alex Eng J. 2023;72:117–134. doi: 10.1016/j.aej.2023.03.065
  • Li B, Liang H, Shi L, et al. Complex dynamics of kopel model with nonsymmetric response between oligopolists. Chaos Solitons Fractals. 2022;156:111860. doi: 10.1016/j.chaos.2022.111860
  • Sadek L, Sadek O, Talibi Alaoui H, et al. Fractional order modeling of predicting covid-19 with isolation and vaccination strategies in morocco. CMES-Comput Model Eng Sci. 2023;136:1931–1950. doi: 10.32604/cmes.2023.025033
  • He Q, Zhang X, Xia P, et al. A comparison research on dynamic characteristics of Chinese and American energy prices. J Glob Inf Manag. 2023;31(1):1–16. doi: 10.4018/JGIM
  • Li B, Liang H, He Q. Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model. Chaos Solitons Fractals. 2021;146:110856. doi: 10.1016/j.chaos.2021.110856
  • Ansari KJ, Asma FI, Shah K, et al. On new updated concept for delay differential equations with piecewise Caputo fractional-order derivative. Waves in Random and Complex Media; 2023. p. 1–20.
  • Li B, Zhang Y, Li X, et al. Bifurcation analysis and complex dynamics of a Kopel triopoly model. J Comput Appl Math. 2023;426:115089. doi: 10.1016/j.cam.2023.115089
  • Karaagac B, Owolabi k.M. . Numerical analysis of polio model: a mathematical approach to epidemiological model using derivative with Mittag–Leffler Kernel. Math Methods Appl Sci. 2023;46(7):8175–8192. doi: 10.1002/mma.7607
  • Karaagac B, Owolabi KM, Nisar KS. Analysis and dynamics of illicit drug use described by fractional derivative with Mittag-Leffler kernel. CMC-Comput Mater Cont. 2020;65(3):1905–1924. doi: 10.32604/cmc.2020.011623
  • Li B, Eskandari Z, Avazzadeh Z. Dynamical behaviors of an SIR epidemic model with discrete time. Fractal Fract. 2022;6(11):659. doi: 10.3390/fractalfract6110659
  • Owolabi KM. Analysis and simulation of herd behaviour dynamics based on derivative with nonlocal and nonsingular kernel. Results Phys. 2021;22:103941. doi: 10.1016/j.rinp.2021.103941
  • He Q, Xia PF, Hu C, et al. PUBLIC information, actual intervention and inflation expectations. Transform Bus Econ. 2022;21(3C):644–666. http://www.transformations.knf.vu.lt/57c/article/publ
  • Jiang X, Li J, Li B, et al. Bifurcation, chaos, and circuit realisation of a new four-dimensional memristor system. Int J Nonlinear Sci Numer Simul; 2022. doi: 10.1515/ijnsns-2021-0393
  • Kanno R. Representation of random walk in fractal space-time. Phys A Stat Mech Appl. 1998;248(1-2):165–175. doi: 10.1016/S0378-4371(97)00422-6
  • Chen W, Sun H, Zhang X, et al. Anomalous diffusion modeling by fractal and fractional derivatives. Comput Math Appl. 2010;59(5):1754–1758. doi: 10.1016/j.camwa.2009.08.020
  • Sun HG, Meerschaert MM, Zhang Y, et al. A fractal Richards' equation to capture the non-Boltzmann scaling of water transport in unsaturated media. Adv Water Resour. 2013;52:292–295. doi: 10.1016/j.advwatres.2012.11.005
  • Atangana A. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Solitons Fractals. 2017;102:396–406. doi: 10.1016/j.chaos.2017.04.027
  • Etemad S, Shikongo A, Owolabi KM, et al. A new fractal-fractional version of giving up smoking model: application of lagrangian piece-wise interpolation along with asymptotical stability. Mathematics. 2022;10(22):4369. doi: 10.3390/math10224369
  • Li B, Eskandari Z. . Dynamical analysis of a discrete-time SIR epidemic model. J Frankl Inst. 2023;360(12):7989–8007. doi: 10.1016/j.jfranklin.2023.06.006
  • Atangana A, Akg'ul A, Owolabi KM. Analysis of fractal fractional differential equations. Alex Eng J. 2020;59(3):1117–1134. doi: 10.1016/j.aej.2020.01.005
  • Rahman Mur. Generalized fractal–fractional order problems under non-singular Mittag-Leffler kernel. Results Phys. 2022;35:105346. doi: 10.1016/j.rinp.2022.105346
  • Mahmood T, Rahman Mu, Arfan M, et al. Mathematical study of algae as a bio-fertilizer using fractal–fractional dynamic model. Math Comput Simul. 2023;203:207–222. doi: 10.1016/j.matcom.2022.06.028
  • Zhang L, Rahman Mu, Haidong Q, et al. Fractal-fractional anthroponotic cutaneous leishmania model study in sense of caputo derivative. Alex Eng J. 2022;61(6):4423–4433. doi: 10.1016/j.aej.2021.10.001
  • Owolabi KM, Shikongo A. Fractal fractional operator method on HER2+ breast cancer dynamics. Int J Appl Comput Math. 2021;7(3):85. doi: 10.1007/s40819-021-01030-5
  • Owolabi KM, Atangana A, Akgul A. Modelling and analysis of fractal-fractional partial differential equations: application to reaction-diffusion model. Alex Eng J. 2020;59(4):2477–2490. doi: 10.1016/j.aej.2020.03.022
  • Adnan AA, Rahman Mur, Arfan M, et al. Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittag-Leffler kernel. Alex Eng J. 2022;61(10):7771–7779. doi: 10.1016/j.aej.2022.01.030
  • Qu H, Rahman Mur, Arfan M, et al. Investigating fractal-fractional mathematical model of tuberculosis (TB) under fractal-fractional Caputo operator. Fractals. 2022;30(05):2240126. doi: 10.1142/S0218348X22401260
  • Liu P, Rahman Mur, Din A. Fractal fractional based transmission dynamics of COVID-19 epidemic model. Comput Methods Biomech Biomed Eng. 2022;25(16):1852–1869. doi: 10.1080/10255842.2022.2040489
  • Gomez-Aguilar JF. Chaos and multiple attractors in a fractal–fractional Shinriki's oscillator model. Phys A Stat Mech Appl. 2020;539:122918. doi: 10.1016/j.physa.2019.122918
  • Abdeljawad T, Baleanu D. Discrete fractional differences with nonsingular discrete Mittag-Leffler kernels. Adv Differ Equ. 2016;2016:1–18. doi: 10.1186/s13662-016-0949-5
  • Van den Driessche P, Watmough J. Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math Biosci. 2002;180(1-2):29–48. doi: 10.1016/S0025-5564(02)00108-6
  • Chitnis N, Cushing JM, Hyman JM. Bifurcation analysis of a mathematical model for malaria transmission. SIAM J Appl Math. 2006;67(1):24–45. doi: 10.1137/050638941
  • Shah K, Alqudah MA, Jarad F, et al. Semi-analytical study of pine wilt disease model with convex rate under Caputo–Febrizio fractional order derivative. Chaos Solitons Fractals. 2020;135:109754. doi: 10.1016/j.chaos.2020.109754