Analysis of an Electrical Circuit Using Two-Parameter Conformable Operator in the Caputo Sense

• Main Authors: Ewa Piotrowska, Łukasz Sajewski
• Format: Article
• Language: English
• Published: MDPI AG 2021-04-01
• Series: Symmetry
• Subjects: pseudo-capacitance; fractional; electrical circuit; two-parameter operator; conformable derivative
• Online Access: https://www.mdpi.com/2073-8994/13/5/771

The problem of voltage dynamics description in a circuit containing resistors, and at least two fractional order elements such as supercapacitors, supplied with constant voltage is addressed. A new operator called Conformable Derivative in the Caputo sense is used. A state solution is proposed. The considered operator is a generalization of three derivative definitions: classical definition (integer order), Caputo fractional definition and the so-called Conformable Derivative (CFD) definition. The proposed solution based on a two-parameter Conformable Derivative in the Caputo sense is proven to be better than the classical approach or the one-parameter fractional definition. Theoretical considerations are verified experimentally. The cumulated matching error function is given and it reveals that the proposed CFD–Caputo method generates an almost two times lower error compared to the classical method.