Matouk A E
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
College of Engineering, Majmaah University, Al-Majmaah, 11952, Saudi Arabia.
Heliyon. 2023 Jul 31;9(8):e18645. doi: 10.1016/j.heliyon.2023.e18645. eCollection 2023 Aug.
In this work, variety of complex dynamics are found in a fractional-order antimicrobial resistance (AMR) model based on the generalized Gamma function. Firstly, the extended left and right Caputo fractional differential operators, respectively, ELCFDO and ERCFDO are introduced. The basic features of the ELCFDO are outlined. The ELCFDO is shown to have a new fractional parameter that affects the occurrence of the complex dynamics in the fractional AMR system. Secondly, discretization of the ELCFDO is studied using piecewise constant arguments. Then, complex dynamics of the discretized version of the fractional AMR system involving the ELCFDO are investigated such as the existence of Neimark-Sacker (NS) and flip bifurcations, the existence of closed invariant curves (CIC), the existence of strange attractors with fractal or multi-fractal structures, and chaotic attractors. Finally, an extension of the fractal-fractional operator (FFO) that combines fractal and fractional differentiation is carried out based on the generalized Gamma function. The extended FFO (EFFO) is applied to the proposed AMR system, which also generates similar complex dynamics.
在这项工作中，基于广义伽马函数的分数阶抗菌耐药性（AMR）模型中发现了多种复杂动力学。首先，分别引入了扩展的左、右卡普托分数阶微分算子，即ELCFDO和ERCFDO。概述了ELCFDO 的基本特征。结果表明，ELCFDO有一个新的分数阶参数，它影响分数阶AMR系统中复杂动力学的出现。其次，利用分段常数变量研究了ELCFDO的离散化。然后，研究了包含ELCFDO的分数阶AMR系统离散版本的复杂动力学，如涅马克-萨克（NS）和翻转分岔的存在性、封闭不变曲线（CIC）的存在性、具有分形或多重分形结构的奇怪吸引子的存在性以及混沌吸引子。最后，基于广义伽马函数对结合了分形和分数阶微分的分形-分数阶算子（FFO）进行了扩展。将扩展的FFO（EFFO）应用于所提出的AMR系统，该系统也产生了类似的复杂动力学。
