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

J.F. Gómez-Aguilar

Chaos, Solitons & Fractals, 2017, vol. 95, issue C, 179-186

Abstract: 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.

Keywords: Irving–Mullineux oscillator; Atangana–Baleanu fractional operators; Sumudu transform; Sumudu-Picard iterative method (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:95:y:2017:i:c:p:179-186

DOI: 10.1016/j.chaos.2016.12.025

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