A different approach for behavior of fractional plant virus model
Volume 15, Issue 3, pp 186--202
http://dx.doi.org/10.22436/jnsa.015.03.02
Publication Date: March 09, 2022
Submission Date: December 15, 2021
Revision Date: January 10, 2022
Accteptance Date: January 20, 2022
Authors
I. Koca
- Department of Accounting and Financial Management, Seydikemer School of Applied Sciences, Mugla Sitki Kocman University, Mugla, Turkey.
H. Bulut
- Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkey.
E. Akcetin
- Department of Accounting and Financial Management, Seydikemer School of Applied Sciences, Mugla Sitki Kocman University, Mugla, Turkey.
Abstract
In the last few decades many authors
pointed out that derivatives and integrals of non-integer order are very
suitable for the description of properties of various real problems. It has
been shown that fractional-order models are more adequate than previously used
integer-order models. In this work, we aim to investigate of different
features of the plant virus model with its fractional order equivalent. We
present an application for reproduction number for these kind of epidemic
models with next generation matrix method. Also, existence and uniqueness of
solutions have been showed for this fractional order system. Finally we
present some figures according to the given numerical scheme.
Share and Cite
ISRP Style
I. Koca, H. Bulut, E. Akcetin, A different approach for behavior of fractional plant virus model, Journal of Nonlinear Sciences and Applications, 15 (2022), no. 3, 186--202
AMA Style
Koca I., Bulut H., Akcetin E., A different approach for behavior of fractional plant virus model. J. Nonlinear Sci. Appl. (2022); 15(3):186--202
Chicago/Turabian Style
Koca, I., Bulut, H., Akcetin, E.. "A different approach for behavior of fractional plant virus model." Journal of Nonlinear Sciences and Applications, 15, no. 3 (2022): 186--202
Keywords
- Fractional differential equation
- existence and uniqueness
- numerical approximation
MSC
References
-
[1]
B. S. T. Alkahtani, I. Koca, A new numerical scheme applied on re-visited nonlinear model of predator-prey based on derivative with non-local and non-singular kernel, Discrete Contin. Dyn. Syst. Ser. S, 13 (2020), 429--442
-
[2]
B. Chen-Charpentier, Stochastic Modeling of Plant Virus Propagation with Biological Control, Mathematics, 9 (2021), 14 pages
-
[3]
M. A. Dokuyucu, Analysis of a Fractional Plant-Nectar-Pollinator Model with the Exponential Kernel, Eastern Anatol. J. Sci., 6 (2020), 11--20
-
[4]
M. A. Dokuyucu, Caputo and Atangana-Baleanu-Caputo Fractional Derivative Applied to Garden Equation, Turkish J. Sci., 5 (2020), 1--7
-
[5]
M. A. Dokuyucu, E. Çelik, Analyzing a novel coronavirus model (Covid-19) in the sense of Caputo Fabrizio fractional operator, Appl. Comput. Math., 20 (2021), 49--69
-
[6]
A. Fereres, Insect vectors as drivers of plant virus emergence, Curr. Opin. Virol., 10 (2015), 42--46
-
[7]
M. Jeger, F. Van Den Bosch, L. Madden, J. Holt, A model for analysing plant-virus transmission characteristics and epidemic development, Math. Med. Biol. A J. IMA, 15 (1998), 1--8
-
[8]
I. Koca, E. Akcetin, P. Yaprakdal, Numerical approximation for the spread of SIQR model with Caputo fractional order derivative, Turkish J. Sci., 5 (2020), 124--139
-
[9]
I. Podlubny, Fractional Differential Equations, Acedemic Press, San Diego (1999)
-
[10]
K. B. G. Scholthof, S. Adkins, H. Czosnek, P. Palukaitis, E. Jacquot, T. Hohn, B. Hohn, K. Saunders, T. Candresse, P. Ahlquist, C. Hemenwat, G. D. Foster, Top 10 plant viruses in molecular plant pathology, Mol. Plant Pathol., 12 (2011), 938--954
-
[11]
P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosc., 180 (2002), 29--48