Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel

Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel

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 tran...

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Main Authors: Abdon Atangana, Badr Saad T Alkahtani
Format: Article
Language:English
Published: SAGE Publishing 2015-06-01
Series:Advances in Mechanical Engineering
Online Access:https://doi.org/10.1177/1687814015591937
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spelling doaj-b5e5651b64b7457cbd912db51e1d60b12020-11-25T03:13:34ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402015-06-01710.1177/168781401559193710.1177_1687814015591937Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernelAbdon Atangana0Badr Saad T Alkahtani1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South AfricaDepartment of Mathematics, Science Colleges, King Saud University, Riyadh, Saudi ArabiaWe 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.https://doi.org/10.1177/1687814015591937
collection DOAJ
language English
format Article
sources DOAJ
author Abdon Atangana
Badr Saad T Alkahtani
spellingShingle Abdon Atangana
Badr Saad T Alkahtani
Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
Advances in Mechanical Engineering
author_facet Abdon Atangana
Badr Saad T Alkahtani
author_sort Abdon Atangana
title Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
title_short Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
title_full Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
title_fullStr Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
title_full_unstemmed Extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
title_sort extension of the resistance, inductance, capacitance electrical circuit to fractional derivative without singular kernel
publisher SAGE Publishing
series Advances in Mechanical Engineering
issn 1687-8140
publishDate 2015-06-01
description 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.
url https://doi.org/10.1177/1687814015591937
work_keys_str_mv AT abdonatangana extensionoftheresistanceinductancecapacitanceelectricalcircuittofractionalderivativewithoutsingularkernel
AT badrsaadtalkahtani extensionoftheresistanceinductancecapacitanceelectricalcircuittofractionalderivativewithoutsingularkernel
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