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An application of the Atangana-Baleanu fractional derivative in mathematical biology: A three-species predator-prey model      
Yazarlar
Behzad Ghanbarı
Türkiye
Doç. Dr. Hatıra GÜNERHAN Doç. Dr. Hatıra GÜNERHAN
Kafkas Üniversitesi, Türkiye
Harı Mohan Srıvastava
Türkiye
Özet
In recent decades, studying the behavior of biological species has become one of the most fascinating areas of applied mathematics. The high importance of conservation of rare species in nature has prompted researchers in various fields to pay particular attention to this issue. Therefore, it is essential to develop mathematical models that examine the dynamics of their behavior. On the other hand, the development of new concepts in numerical analysis has enabled us to preserve more information on the evolutionary behavior history of a dynamic system and to use it in predicting the new features of the system. Fractional derivatives have provided such a valuable tool. This paper studies a dynamic system that models the interactions between two densities of immature and mature prey and predator populations. In the model, prey population is divided into two populations, including mature prey and immature prey. Another feature of the model is that predator depends on mature prey only and it followed by Crowley-Martin type functional response. Moreover, the fractional operator used in this model as derivative is of the Atangana-Baleanu AB type. Using this kind of fractional derivative causes the results to depend on the fractional order of the derivative. The addition of the concept of memory to the model is another highlight of using this type of derivative for the biological model. This helps the model to apply all the essential information of the phenomenon from the beginning to the desired time in the calculations. Existence and uniqueness of solutions to the fractional model are also investigated in this manuscript. The numerical method used in the article is also one of the most efficient patterns in solving problems with fractional derivatives. Using this effective method makes the results very consistent with what we actually expect to happen. Many simulations have been carried out to investigate the effect of parameters in the model on its overall behavior. Numerical results show the impressive performance of the fractional operator on the dynamic behavior of the considered predator-prey model. This efficient fractional operator can also be tested in the structure of other existing biological models.
Anahtar Kelimeler
Approximate solutions | Atangana-Baleanu derivative | Computational approach | Mathematical biology | Non-local and Non-singular kernels | Predator and prey model
Makale Türü Özgün Makale
Makale Alt Türü SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale
Dergi Adı Chaos, Solitons & Fractals
Dergi ISSN 0960-0779
Dergi Tarandığı Indeksler SCI-Expanded
Makale Dili İngilizce
Basım Tarihi 09-2020
Cilt No 138
Sayı 1
Sayfalar 109910 / 0
Doi Numarası 10.1016/j.chaos.2020.109910
Makale Linki http://dx.doi.org/10.1016/j.chaos.2020.109910