Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2024, Sayı: 1, 1 - 14, 01.10.2024
https://doi.org/10.46810/tdfd.1402905

Öz

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.

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

Yıl 2024, Sayı: 1, 1 - 14, 01.10.2024
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.

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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematiksel Fizik (Diğer)
Bölüm Makaleler
Yazarlar

Mustafa Ali Dokuyucu 0000-0001-9331-8592

Yayımlanma Tarihi 1 Ekim 2024
Gönderilme Tarihi 10 Aralık 2023
Kabul Tarihi 27 Aralık 2023
Yayımlandığı Sayı Yıl 2024 Sayı: 1

Kaynak Göster

APA Dokuyucu, M. A. (2024). Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. Türk Doğa Ve Fen Dergisi(1), 1-14. https://doi.org/10.46810/tdfd.1402905
AMA Dokuyucu MA. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TDFD. Ekim 2024;(1):1-14. doi:10.46810/tdfd.1402905
Chicago Dokuyucu, Mustafa Ali. “Existence and Uniqueness Solution for a Mathematical Model With Mittag-Leffler Kernel”. Türk Doğa Ve Fen Dergisi, sy. 1 (Ekim 2024): 1-14. https://doi.org/10.46810/tdfd.1402905.
EndNote Dokuyucu MA (01 Ekim 2024) Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. Türk Doğa ve Fen Dergisi 1 1–14.
IEEE M. A. Dokuyucu, “Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel”, TDFD, sy. 1, ss. 1–14, Ekim 2024, doi: 10.46810/tdfd.1402905.
ISNAD Dokuyucu, Mustafa Ali. “Existence and Uniqueness Solution for a Mathematical Model With Mittag-Leffler Kernel”. Türk Doğa ve Fen Dergisi 1 (Ekim 2024), 1-14. https://doi.org/10.46810/tdfd.1402905.
JAMA Dokuyucu MA. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TDFD. 2024;:1–14.
MLA Dokuyucu, Mustafa Ali. “Existence and Uniqueness Solution for a Mathematical Model With Mittag-Leffler Kernel”. Türk Doğa Ve Fen Dergisi, sy. 1, 2024, ss. 1-14, doi:10.46810/tdfd.1402905.
Vancouver Dokuyucu MA. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TDFD. 2024(1):1-14.