Fractional electromagnetic waves in circular waveguides with fractional-order inductance characteristics

ABSTRACT

The Maxwell equations play a vital role in the electromagnetic theory. With the development of Fractional Calculus and its applications, new fractional Maxwell equations are required to describe fractional electromagnetic fields. In this paper, the fractional electromagnetic induction law is presented with considering the properties of fractional inductance. Based on this, we have obtained the fractional Maxwell equations. In addition, the non-homogeneous fractional wave equations and the homogeneous fractional vector Helmholtz equations are deduced. Using these results, we investigate the behavior of electromagnetic waves in fractional circular waveguides with fractional-order inductance characteristics. The results show that the electromagnetic fields change with different fractional orders.

KEYWORDS:

• Wave propagation
• fractional Maxwell equations
• fractional-order inductance
• circular waveguides

SUBJECT CLASSIFICATIONS CODES:

• PACS: 03.50.De
• 45.10.Hj
• 41.20.Jb
• 84.32.Hh

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Bo Zhang http://orcid.org/0000-0001-9172-698X

Chao Rong http://orcid.org/0000-0002-5754-301X

Additional information

Funding

This project was supported by the Key Program of National Natural Science Foundation of China (grant number 51437005).

Notes on contributors

Chao Rong

Chao Rong was born in Shanxi, China, in 1995. He received the BS degree in electrical engineering and automation from the South China University of Technology, Guangzhou, China, in 2018, where he is currently pursuing the MS degree in power electronics and power drives. His current research interests include nonlinear analysis and wireless power transfer technology.

Bo Zhang

Bo Zhang was born in Shanghai, China, in 1962. He received the BSc degree in electrical engineering from Zhejiang University, Hangzhou, China, in 1982, the MSc degree in power electronics from Southwest Jiaotong University, Chengdu, China, in 1988, and the PhD degree in power electronics from the Nanjing University of Aeronautics and Astronautics, Nanjing, China, in 1994. He is currently a Professor with the School of Electric Power, South China University of Technology, Guangzhou, China. He has authored or co-authored eight books and over 400 technical papers, and he holds over 100 patents. His current research interests include nonlinear analysis, modeling and control of power electronic converters, and wireless power transfer applications.