吸引子
数学
分形
分数阶微积分
狄拉克三角函数
混乱的
分形导数
分形维数
数学分析
动力系统理论
Mittag-Leffler函数
应用数学
微分算子
物理
计算机科学
分形分析
量子力学
人工智能
作者
Abdon Atangana,Sania Qureshi
标识
DOI:10.1016/j.chaos.2019.04.020
摘要
In this paper, newly proposed differential and integral operators called the fractal–fractional derivatives and integrals have been used to predict chaotic behavior of some attractors from applied mathematics. These new differential operators are convolution of fractal derivative with power law, exponential decay law with Delta-Dirac property and the generalized Mittag-Leffler function with Delta-Dirac property, respectively. These new operators will be able to capture self-similarities in the chaotic attractors under investigation. We presented, in general, three numerical schemes that can be used to solve such systems of nonlinear differential equations. The general conditions for the existence and the uniqueness of the exact solutions are obtained. These new differential and integral operators applied in five selected chaotic attractors with numerical simulations for varying values of fractional order α and the fractal dimension τ have yielded very interesting results. It is to be believed that this research study will open new doors for in-depth investigation in dynamical systems of varying nature.
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