Research Article

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

Number: 1 October 1, 2024
EN

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

Abstract

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.

Keywords

References

  1. 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.
  2. Atangana A, Owolabi KM. New numerical approach for fractional differential equations. Mathematical Modelling of Natural Phenomena. 2018;13(1):3.
  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.
  4. Bagley RL, Torvik PJ. Fractional calculus in the transient analysis of viscoelastically damped structures. AIAA journal. 1985 Jun;23(6):918-25.
  5. 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.
  6. Campbell GL, Marfin AA, Lanciotti RS, Gubler DJ. West nile virus. The Lancet infectious diseases. 2002 Sep 1;2(9):519-29.
  7. Caputo M. Linear models of dissipation whose Q is almost frequency independent—II. Geophysical Journal International. 1967 Nov 1;13(5):529-39.
  8. Dokuyucu MA. Caputo and atangana-baleanu-caputo fractional derivative applied to garden equation. Turkish Journal of Science. 2020 Mar 3;5(1):1-7.

Details

Primary Language

English

Subjects

Mathematical Physics (Other)

Journal Section

Research Article

Publication Date

October 1, 2024

Submission Date

December 10, 2023

Acceptance Date

December 27, 2023

Published in Issue

Year 2024 Number: 1

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
1.Dokuyucu MA. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TJNS. 2024;(1):1-14. doi:10.46810/tdfd.1402905
Chicago
Dokuyucu, Mustafa Ali. 2024. “Existence and Uniqueness Solution for a Mathematical Model With Mittag-Leffler Kernel”. Türk Doğa Ve Fen Dergisi, no. 1: 1-14. https://doi.org/10.46810/tdfd.1402905.
EndNote
Dokuyucu MA (October 1, 2024) Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. Türk Doğa ve Fen Dergisi 1 1–14.
IEEE
[1]M. A. Dokuyucu, “Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel”, TJNS, no. 1, pp. 1–14, Oct. 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 (October 1, 2024): 1-14. https://doi.org/10.46810/tdfd.1402905.
JAMA
1.Dokuyucu MA. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TJNS. 2024;:1–14.
MLA
Dokuyucu, Mustafa Ali. “Existence and Uniqueness Solution for a Mathematical Model With Mittag-Leffler Kernel”. Türk Doğa Ve Fen Dergisi, no. 1, Oct. 2024, pp. 1-14, doi:10.46810/tdfd.1402905.
Vancouver
1.Mustafa Ali Dokuyucu. Existence and Uniqueness Solution for a Mathematical Model with Mittag-Leffler Kernel. TJNS. 2024 Oct. 1;(1):1-14. doi:10.46810/tdfd.1402905

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