A fractional mathematical model of breast cancer competition model. (October 2019)

• Record Type: Journal Article
• Authors: Solís-Pérez, J.E.; Gómez-Aguilar, J.F.; Atangana, A.
• Is Part Of: Chaos, solitons and fractals. Volume 127(2019)
• Page Start: 38
• Page End: 54
• Publication Date: 2019-10
• Subjects: Fractional derivatives and integrals -- Integral transforms -- Laplace transform -- Breast cancer competition model; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2019.06.027
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Adaptive fractional control is design to synchronize chimera states. Atangana–Baleanu fractional derivative with Mittag-Leffler (M-L) kernel is considered. Numerical simulations are presented for specific parameters. The adaptive controller is based on the uncertainty of the coupling parameters. Abstract: In this paper, a mathematical model which considers population dynamics among cancer stem cells, tumor cells, healthy cells, the effects of excess estrogen and the body's natural immune response on the cell populations was considered. Fractional derivatives with power law and exponential decay law in Liouville–Caputo sense were considered. Special solutions using an iterative scheme via Laplace transform were obtained. Furthermore, numerical simulations of the model considering both derivatives were obtained using the Atangana–Toufik numerical method. Also, random model described by a system of random differential equations was presented. The use of fractional derivatives provides more useful information about the complexity of the dynamics of the breast cancer competition model.