Open AccessExtension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
Author(s) -
Abdon Atangana,
Badr Saad T. Alkahtani
Publication year - 2015
Publication title -
advances in mechanical engineering/advances in mechanical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.318
H-Index - 40
eISSN - 1687-8140
pISSN - 1687-8132
DOI - 10.1177/1687814015591937
Subject(s) - laplace transform , inductance , capacitance , fractional calculus , derivative (finance) , mathematics , mathematical analysis , equivalent series inductance , kernel (algebra) , equivalent circuit , physics , engineering , electrical engineering , pure mathematics , voltage , electrode , quantum mechanics , financial economics , economics
We presented the model of resistance, inductance, capacitance circuit using a novel derivative with fractional order that was recently proposed by Caputo and Fabrizio. The derivative possesses more important characteristics that are very useful in modelling. In this article, we proposed a novel translation from ordinary equation to fractional differential equation. Using this novel translation, we modified the resistance, inductance, capacitance electricity model. We solved analytically the modified equation using the Laplace transform method. We presented numerical results for different values of the fractional order. We observed that this solution depends on the fractional order