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Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System

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Fractional Derivatives with Mittag-Leffler Kernel

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 194))

Abstract

The Atangana–Baleanu fractional differential and integral operators have been used in this chapter to describe the crossover behavior of a chaotic complex system. The existing model was extended and modified by replacing the conventional time local operator by the fractional differential operator with non-local and non-singular kernel. We established the conditions under which the existence of a uniquely exact solution can be found. A newly established numerical scheme was used to solve the modified model and numerical solutions are displayed for different values of fractional order.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Mehmet Akif Ersoy University, 15100, Burdur, Turkey

    Ilknur Koca

  2. Faculty of Natural and Agricultural Sciences, Institute of Groundwater Studies, University of Free State, Bloemfontein, 9301, South Africa

    A. Atangana

Authors
  1. Ilknur Koca
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  2. A. Atangana
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Correspondence to Ilknur Koca .

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Editors and Affiliations

  1. CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    José Francisco Gómez

  2. CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Lizeth Torres

  3. Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Morelos, Mexico

    Ricardo Fabricio Escobar

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Koca, I., Atangana, A. (2019). Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System. In: Gómez, J., Torres, L., Escobar, R. (eds) Fractional Derivatives with Mittag-Leffler Kernel. Studies in Systems, Decision and Control, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-030-11662-0_7

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  • DOI: https://doi.org/10.1007/978-3-030-11662-0_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-11661-3

  • Online ISBN: 978-3-030-11662-0

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