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.

Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental resultsIncludes circuits and systems based on new nonlinear elementsCovers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchersCloses the gap between theoretical approaches and real-world applicationsProvides MATLAB® and Simulink code for many applications in the book

1. Analog and digital realization of nonlinear fractional order systems 2. Bifurcation analysis and control 3. Chaos analysis, control and anti-control 4. Chaos modeling and control applications 5. Control and synchronization of complex networks 6. Discrete chaotic maps and their applications 7. Fractional order modelling of physical systems 8. Fractional system identification and optimization 9. Fuzzy fractional order controller 10. Nonlinear circuit analysis and applications 11. Random number generators and encryption in integer and fractional order domains 12. Recent nontechnology applications based on memristors, memcapacitors, and meminductor elements