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Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel Read chapter Read first chapter

2019 | OriginalPaper | Chapter

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

Authors : Ilknur Koca, A. Atangana

Published in: Fractional Derivatives with Mittag-Leffler Kernel

Publisher: Springer International Publishing

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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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Metadata
Title
Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System
Authors
Ilknur Koca
A. Atangana
Copyright Year
2019
Book
Fractional Derivatives with Mittag-Leffler Kernel

Print ISBN: 978-3-030-11661-3

Electronic ISBN: 978-3-030-11662-0

Copyright Year: 2019

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