Fractional-Order Electrical Circuit Theory

1. Front Matter

   Pages i-xv

   PDF

2. Introduction to Fractional Calculus

   • Bo Zhang, Xujian Shu

   Pages 1-38

3. Fractional-Order Components and Their Basic Circuits

   • Bo Zhang, Xujian Shu

   Pages 39-54

4. Theorems of Fractional-Order Circuits

   • Bo Zhang, Xujian Shu

   Pages 55-91

5. Time-Domain Analysis of Fractional-Order Circuits

   • Bo Zhang, Xujian Shu

   Pages 93-164

6. Sinusoidal Steady-State Analysis of Fractional-Order Circuits

   • Bo Zhang, Xujian Shu

   Pages 165-185

7. Sinusoidal Steady-State Analysis of Three-Phase Fractional-Order Circuits

   • Bo Zhang, Xujian Shu

   Pages 187-226

8. Non-sinusoidal Periodic Steady-State Analysis of Fractional-Order Circuits

   • Bo Zhang, Xujian Shu

   Pages 227-248

9. Two-Port Fractional-Order Networks

   • Bo Zhang, Xujian Shu

   Pages 249-283

10. State-Variable Analysis of Fractional-Order Circuits

    • Bo Zhang, Xujian Shu

    Pages 285-299

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. 

• Fractional-order
• Fractional Calculus Theory
• Fractional-order Dynamic Electrical Circuits
• Fractional-order Three-phase Sinusoidal Electrical Circuits
• Fractional-order Two-port Network.

• School of Electric Power, South China University of Technology, Guangzhou, China

  Bo Zhang, Xujian Shu

Bo Zhang was born in Shanghai, China, in 1962. He received the B.S. degree in electrical engineering from Zhejiang University, Hanzhou, China, in 1982, the M.S. degree in power electronics from Southwest Jiaotong University, Chengdu, China, in 1988, and the Ph.D. degree in power electronics from Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1994.  He is currently a Professor and the Vice Dean in the School of Electric Power, South China University of Technology, Guangzhou, China.  He has authored or coauthored 10 books, more than 600 papers and 130 patents. His current research interests include nonlinear analysis and control of power electronics, wireless power transfer technology, and ac drives.

Xujian Shu was born in Zongyang, Tongling, China, in 1993. She received the B.S. degree in electrical engineering from China University of Mining and Technology, Xuzhou, China, in 2015. She is currently a Doctor in the School of Electric Power, South China University of Technology, Guangzhou, China. She has authored 7 papers and 6 patents. Her current research interests include wireless power transfer and fractional-order calculus.

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