In the nineteenth-century, fractional calculus had its origin in extending differentiation and integration operators from the integer-order case to the fractional-order case. Discrete fractional calculus has recently become an important research topic, useful in various science and engineering applications. The first definition of the fractional-order discrete-time/difference operator was introduced in 1974 by Diaz and Osler, where such operator was derived by discretizing the fractional-order continuous-time operator. Successfully, several types of fractional-order difference operators have then been proposed and introduced through further generalizing numerous classical operators, motivating several researchers to publish extensively on a new class of systems, viz the nonlinear fractional-order discrete-time systems (or simply, the fractional-order maps), and their chaotic behaviors. This discovery of chaos in such maps, has led to novel control methods for effectively stabilizing their chaotic dynamics. The aims of this book are as follows: Presenting the recent developments, trends, research solutions, applications and open problems related to fractional-order chaotic maps; Illustrating many interdisciplinary applications, like modulization, control, circuits, security and encryption; Including all theories associated with chaos, control and synchronization of discrete-time systems; Providing a useful reference on the topic of fractional-order chaotic maps and their applications.
Dr Adel Ouannas received his PhD in Dynamical Systems from Constantine University. He is currently Professor of Applied Mathematics at the University of Oum El Bouaghi in Algeria. Dr Ouannas has his main research interests in the fields of chaos theory, control, synchronization, and fractional order calculus. He has published more than 300 research papers in scientific journals and national and international conferences.
Iqbal M Batiha holds a MSc in applied mathematics (2014) from Al al-Bayt University, and a PhD (2019) from The University of Jordan. He is a founding member of the international center for scientific researches and studies (ICSRS-Jordan), and he is currently working as an assistant professor at the Department of Mathematics in Al Zaytoonah University of Jordan as well as he is also working at the Nonlinear Dynamics Research Center (NDRC) that recently established at Ajman University. He has published several papers in different peer reviewed international journals. Iqbal M Batiha was awarded several prizes including the Riemann-Liouville Award which was presented from the International Conference on Fractional Differentiation and its Applications (ICFDA'18) that was held in Amman on July 2018, and the Oliviu Gherman Award which was presented from the First Online Conference on Modern Fractional Calculus and Its Applications that held in Turkey on December 2020. He is currently serving furthermore on the board of the International Journal of Open Problems in Computer Science and Mathematics (IJOPCM), and the editorial review boards of several international journals.
Viet-Thanh Pham graduated in electronics and telecommunications from the Hanoi University of Technology, Vietnam, in 2005. He received the PhD degree in electronics, automation and control of complex systems engineering from the University of Catania, Italy, in 2013. He is currently working at the Faculty of Electrical and Electronics Engineering, Ton Duc Thang University. His scientific research interests include chaos, nonlinear control, applications of nonlinear systems, analysis and design of analog circuits, and FPGA-based digital circuits.
