Fractional-Order Electrical Circuit Theory

This book presents a concise and insightful view of the knowledge on fractional-order electrical circuits, which belongs to the subject of Electric Engineering and involves mathematics of fractional calculus. It offers an overview of fractional calculus and then describes and analyzes the basic theories and properties of fractional-order elements and fractional-order electrical circuit composed of fractional-order elements. Therein, the fundamental theorems, time-domain analysis, steady-state analysis, complex frequency domain analysis and state variable analysis of fractional-order electrical circuit are included. The fractional-order two-port networks and generalized fractional-order linear electrical circuits are also mentioned. Therefore, this book provides readers with enough background and understanding to go deeper into the topic of fractional-order electrical circuit, so that it is useful as a textbook for courses related to fractional-order elements, fractional-order electrical circuits, etc. This book is intended for students without an extensive mathematical background and is suitable for advanced undergraduate and graduate students, engineers and researchers who focus on the fractional-order elements, electrical circuits and systems.

Autorentext

Jin Peng is a leading professor at Huanggang Normal University, Hubei, China. He received his Ph.D. degree in operational research and cybernetics from Tsinghua University in 2003. His primary research interests include uncertainty theory, uncertain programming, uncertain risk analysis, uncertain network optimization, intelligent computing and uncertainty modelling in various application areas such as scheduling, vehicle routing problems, finance. Dr. Peng has published more than 100 research papers on a range of topics in various international academic journals including European Journal of Operational Research, International Journal of Production Research, Information Sciences, Applied Mathematical Modelling, Applied Mathematics and Computation, Insurance: Mathematics and Economics, Fuzzy Optimization and Decision Making, Soft Computing, Applied Soft Computing, Journal of Intelligent Manufacturing, Computers & Industrial Engineering, International Journal of Computer Mathematics, International Journal of Systems Science, International Journal of General Systems, International Journal of Machine Learning and Cybernetics, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, etc. His research has been supported by varieties of research projects including the National Natural Science Foundation, the Humanity and Social Science Foundation of Ministry of Education, and Hubei Provincial Natural Science Foundation, China. Prof. Peng is currently serving as the associate editor, area editor, editorial board member, or peer reviewer of multiple international journals. He has also acted as the chairs, board members of program committees or organizing committees in various conferences or academic organizations at home and abroad.

Inhalt
Overview of Fractional Calculus Theory.- Fractional-order Electrical Circuits and Their Fundamental Laws.- Network Theorems of Fractional-order Electrical Circuits.- Time-domain Analysis of Fractional-order Dynamic Electrical Circuits.- Sinusoidal Steady-state Analysis of Fractional-order Electrical Circuits.- Fractional-order Three-phase Sinusoidal Electrical Circuits.- Analysis of Periodic Non-sinusoidal Steady-state Fractional-order Electrical Circuits.- Fractional-order Two-port Network.- Complex Frequency Domain Analysis of Fractional-order Electrical Circuits.- State Variable Analysis Method of Fractional-order Electrical Circuits.- Fractional-order Generalized Linear Electrical Circuits and Their Properties.