Irving-Mullineux oscillator via fractional derivatives with Mittag-Leffler kernel

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• 作者：J.F. Gó ; mez-Aguilar ^{jgomez@cenidet.edu.mx jfranciscogoma@hotmail.com}
• 关键词：Irving&ndash ; Mullineux oscillator ; Atangana&ndash ; Baleanu fractional operators ; Sumudu transform ; Sumudu-Picard iterative method
• 刊名：Chaos, Solitons & Fractals
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：95
• 期：Complete
• 页码：179-186
• 全文大小：2182 K
• 卷排序：95

文摘

Recently, Abdon Atangana and Dumitru Baleanu suggested a novel fractional operator based in the Mittag-Leffler function with non-singular and nonlocal kernel. In this paper using the newly established fractional operator, an alternative representation of the Irving–Mullineux oscillator via Atangana–Baleanu fractional derivative in Liouville–Caputo sense is presented. Numerical simulations are obtained using an iterative scheme via Sumudu-Picard iterative method. The existence and uniqueness of the solutions are studied in detail using the fixed-point theorem and some properties of the inner product and the Hilbert space. Numerical simulations of the special solutions were done and new chaotic behaviors are obtained.