A New Look at the Capacitor Theory

Fractal and Fractional

article

Manuel Duarte Ortigueira¹  Valeriy Martynyuk²  Volodymyr Kosenkov²  Arnaldo Guimarães Batista¹ 

[1] CTS-UNINOVA and DEE, NOVA School of Science and Technology of NOVA University of Lisbon;Khmelnitsky National University

关键词: fractional capacitor;    fractional inductor;    fractional derivative;    fractor;    Davidson–Cole model;    tempered derivative;   

DOI  :  10.3390/fractalfract7010086

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

The mathematical description of the charging process of time-varying capacitors is reviewed and a new formulation is proposed. For it, suitable fractional derivatives are described. The case of fractional capacitors that follow the Curie–von Schweidler law is considered. Through suitable substitutions, a similar scheme for fractional inductors is obtained. Formulae for voltage/current input/output are presented. Backward coherence with classic results is established and generalised to the variable order case. The concept of a tempered fractor is introduced and related to the Davidson–Cole model.

【 授权许可】

CC BY