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

  • Ilknur KocaEmail author
  • A. Atangana
Chapter
Part of the Studies in Systems, Decision and Control book series (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.

Keywords

Fractional calculus Atangana–Baleanu fractional derivative Chaotic complex system 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesMehmet Akif Ersoy UniversityBurdurTurkey
  2. 2.Faculty of Natural and Agricultural SciencesInstitute of Groundwater Studies, University of Free StateBloemfonteinSouth Africa

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