Chaos theory describes the dynamical systems which exhibit unpredictable, yet deterministic, behavior. Chaotic systems have a remarkable importance in both modeling and information processing in many fields. Fractional calculus has also become a powerful tool in describing the dynamics of complex systems such as fractional order (FO) chaotic systems. The FO parameter adds extra degrees of freedom which increases the design flexibility and adds more control on the design. The extra parameters increase the chaotic range. This chapter provides a review of several generalized discrete time one-dimensional maps. The generalizations include a signed control parameter, scaling parameters, and shaping parameters. The properties of the generalized fractional logistic map are presented. The generalized fractional tent map is presented and its properties are studied and validated using numerical simulations. Various simulations are conducted including time series, bifurcation diagrams, and various chaotic properties against the system parameters and FO parameter. © 2018 Elsevier Inc. All rights reserved.
Modified methods for solving two classes of distributed order linear fractional differential equations
This paper introduces two methods for the numerical solution of distributed order linear fractional differential equations. The first method focuses on initial value problems (IVPs) and based on the ?th Caputo fractional definition with the shifted Chebyshev operational matrix of fractional integration. By applying this method, the IVPs are converted into simple linear differential equations which can be easily handled. The other method focuses on boundary value problems (BVPs) based on Picard’s method frame. This method is based on iterative formula contains an auxiliary parameter which provides a simple way to control the convergence region of solution series. Several numerical examples are used to illustrate the accuracy of the proposed methods compared to the existing methods. Also, the response of mechanical system described by such equations is studied. © 2017 Elsevier Inc.
Mathematical techniques of fractional order systems : A volume in advances in nonlinear dynamics and chaos (ANDC)
Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security
Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications
Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. © 2018 Elsevier Inc. All rights reserved.
Mathematical Techniques of Fractional Order Systems
Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. © 2018 Elsevier Inc. All rights reserved.
Design and analysis of 2T2M hybrid CMOS-Memristor based RRAM
In this paper, a Static Noise Margin (SNM) analysis for 2T2M RRAM cell is investigated
Comparison between three approximation methods on oscillator circuits
The promising capabilities of fractional-order devices challenge researchers to find a way to build it physically
A generalized family of memristor-based voltage controlled relaxation oscillator
Recently, memristive oscillators are a significant topic in the nonlinear circuit theory where there is a possibility to build relaxation oscillators without existence of reactive elements
Effect of Different Approximation Techniques on Fractional-Order KHN Filter Design
Having an approximate realization of the fractance device is an essential part of fractional-order filter design and implementation