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Open AccessArticle

Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law

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CONACyT-Tecnológico Nacional de Mexico/CENIDET, Interior Internado Palmira s/n Col. Palmira C.P., Cuernavaca 62490, Mexico
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Tecnológico Nacional de Mexico/CENIDET, Interior Internado Palmira s/n Col. Palmira C.P., Cuernavaca 62490, Mexico
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Department of Mathematics, Faculty of Art and Sciences, Cankaya University, Ankara 06790, Turkey
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Institute of Space Sciences, P.O. Box, MG-23, Magurele-Bucharest R 76900, Romania
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College of Engineering, Mechanics and Materials, Hohai University, Nanjing 210098, China
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Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Dir Upper, Sheringal 18000, Pakistan
*
Authors to whom correspondence should be addressed.
Entropy 2017, 19(12), 681; https://doi.org/10.3390/e19120681
Received: 1 November 2017 / Revised: 3 December 2017 / Accepted: 6 December 2017 / Published: 19 December 2017
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory III)
In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained. View Full-Text
Keywords: cancer model; Caputo-Fabrizio fractional derivative; Atangana-Baleanu fractional derivative; Sumudu-Picard iterative method cancer model; Caputo-Fabrizio fractional derivative; Atangana-Baleanu fractional derivative; Sumudu-Picard iterative method
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MDPI and ACS Style

Gómez-Aguilar, J.F.; López-López, M.G.; Alvarado-Martínez, V.M.; Baleanu, D.; Khan, H. Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law. Entropy 2017, 19, 681. https://doi.org/10.3390/e19120681

AMA Style

Gómez-Aguilar JF, López-López MG, Alvarado-Martínez VM, Baleanu D, Khan H. Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law. Entropy. 2017; 19(12):681. https://doi.org/10.3390/e19120681

Chicago/Turabian Style

Gómez-Aguilar, José F.; López-López, María G.; Alvarado-Martínez, Victor M.; Baleanu, Dumitru; Khan, Hasib. 2017. "Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law" Entropy 19, no. 12: 681. https://doi.org/10.3390/e19120681

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