The RC Circuit Described by Local Fractional Differential Equations

Issue title: Theory and Applications of Fractional Fourier Transform and its Variants

Guest editors: Yudong Zhang, Xiao-Jun Yang, Carlo Cattani, Zhengchao Dong, Ti-Fei Yuan and Liang-Xiu Han

Article type: Research Article

Authors: Zhao, Xiao-Hu^a | Zhang, Yudong^{b; *; †} | Zhao, Duan^c | Yang, Xiaojun^d

Affiliations: [a] IoT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China | [b] School of Computer Science and Technology, Nanjing Normal University, Nanjing, Jiangsu 210023, People’s Republic of China. zhangyudong@njnu.edu.cn | [c] IoT Perception Mine Research Center, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China | [d] Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou 221008, People’s Republic of China

Correspondence: [†] Address for correspondence: 1 Wenyuan, Nanjing, Jiangsu 210023, People’s Republic of China

Note: [*] Also affiliated at: State and Local Joint Engineering Laboratory of Mining Internet Application Technology, Xuzhou 221008, People’s Republic of China

Abstract: A non-differentiable resistor-capacitor circuit comprised of the capacitor and resistor in the fractal-time domain is first proposed in this article. The solution behavior of the corresponding local fractional ordinary differential equation is presented for the Mittag-Leffler decay defined on Cantor sets. The obtained results reveal the sufficiency of the local fractional calculus in the analysis of the fractal electrical systems.

Keywords: ordinary differential equations, Mittag-Leffler decay, electric circuit, local fractional derivative

DOI: 10.3233/FI-2017-1501

Journal: Fundamenta Informaticae, vol. 151, no. 1-4, pp. 419-429, 2017