Fractional order chaotic systems: history, achievements, applications, and future challenges

• Published in: The European physical journal. ST, Special topics Vol. 229; no. 6-7; pp. 887 - 904
• Main Author: Tavazoei, Mohammad Saleh
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-03-2020; Springer Nature B.V
• Subjects: Atomic; Chaos theory; Classical and Continuum Physics; Condensed Matter Physics; Differential equations; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Review; Special Chaotic Systems
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2020-900238-8

Motivated by the importance of study on the complex behaviors, which may be exhibited by fractional order differential equations, this review paper focuses on dynamical fractional order systems exhibiting chaotic behaviors. The review begins with a brief history on the first publications on the above-mentioned subject. Then, the review is continued by investigating the recent progresses relevant to fractional order chaotic systems. Furthermore, a summary on some applications for such systems, which have been reported in the literature, is presented. Finally, the paper is closed by discussing some open problems on the aforementioned research subject. These open problems, as future challenges for further study on fractional order chaotic systems, can specify some direction lines for continuing the research on that subject.