Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel

Yıl 2024, , 1 - 14, 01.10.2024

Mustafa Ali Dokuyucu

https://doi.org/10.46810/tdfd.1402905

Öz

In this work, we analyse the fractional order West Nile Virus model involving the Atangana-Baleanu derivatives. Existence and uniqueness solutions were obtained by the fixed-point theorem. Another impressive aspect of the work is illustrated by simulations of different fractional orders by calculating the numerical solutions of the mathematical model.

Anahtar Kelimeler

Virus, Mathematical Modeling, Fractional derivatives and integrals, Numerical solution

Kaynakça

• Atangana A, Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. Thermal Science. 2016; , 20(2), 763-769.
• Atangana A, Owolabi KM. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena. 2018;13(1):3.
• Bagley RL, Torvik PJ. A theoretical basis for the application of fractional calculus to viscoelasticity. Journal of Rheology. 1983 Jun 1;27(3):201-10.
• Bagley RL, Torvik PJ. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA journal. 1985 Jun;23(6):918-25.
• Bowman C, Gumel AB, Van den Driessche P, Wu J, Zhu H. A mathematical model for assessing control strategies against West Nile virus. Bulletin of mathematical biology. 2005 Sep 1;67(5):1107-33.
• Campbell GL, Marfin AA, Lanciotti RS, Gubler DJ. West nile virus. The Lancet infectious diseases. 2002 Sep 1;2(9):519-29.
• Caputo M. Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International. 1967 Nov 1;13(5):529-39.
• Dokuyucu MA. Caputo and atangana-baleanu-caputo fractional derivative applied to garden equation. Turkish Journal of Science. 2020 Mar 3;5(1):1-7.
• Dokuyucu M, Celik E. Analyzing a novel coronavirus model (COVID-19) in the sense of Caputo-Fabrizio fractional operator. Applied and Computational Mathematics. 2021;20(1).
• Hayes EB, Komar N, Nasci RS, Montgomery SP, O'Leary DR, Campbell GL. Epidemiology and transmission dynamics of West Nile virus disease. Emerging infectious diseases. 2005 Aug;11(8):1167.
• Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. elsevier; 2006 Feb 16.
• Koca İ, Akçetin E, Yaprakdal P. Numerical approximation for the spread of SIQR model with Caputo fractional order derivative. Turkish Journal of Science. 2020;5(2):124-39.
• Koeller R. Applications of fractional calculus to the theory of viscoelasticity. (1984): 299-307.
• Koksal ME. Stability analysis of fractional differential equations with unknown parameters. Nonlinear Analysis: Modelling and Control. 2019 Feb 1;24(2):224-40.
• Koksal ME. Time and frequency responses of non-integer order RLC circuits. AIMS Mathematics. 2019 Jan 1;4(1):64-78.
• Lewis M, Rencławowicz J, den Driessche PV. Traveling waves and spread rates for a West Nile virus model. Bulletin of mathematical biology. 2006 Jan;68:3-23.
• Podlubny I. Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Elsevier; 1998 Oct 27.
• Tarboush AK, Lin Z, Zhang M. Spreading and vanishing in a West Nile virus model with expanding fronts. Science China Mathematics. 2017 May;60:841-60.
• Wonham MJ, de-Camino-Beck T, Lewis MA. An epidemiological model for West Nile virus: invasion analysis and control applications. Proceedings of the royal society of London. Series B: Biological Sciences. 2004 Mar 7;271(1538):501-7.