Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel

Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel

The numerical approximation of the Caputo–Fabrizio fractional derivative with fractional order between 1 and 2 is proposed in this work. Using the transition from ordinary derivative to fractional derivative, we modified the RLC circuit model. The Crank–Nicolson numerical scheme was used to solve th...

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Main Authors: Abdon Atangana, Juan Jose Nieto
Format: Article
Language:English
Published: SAGE Publishing 2015-10-01
Series:Advances in Mechanical Engineering
Online Access:https://doi.org/10.1177/1687814015613758
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spelling doaj-3e9ace18064242b59fbe12f8b21d40272020-11-25T02:52:30ZengSAGE PublishingAdvances in Mechanical Engineering1687-81402015-10-01710.1177/168781401561375810.1177_1687814015613758Numerical solution for the model of RLC circuit via the fractional derivative without singular kernelAbdon Atangana0Juan Jose Nieto1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South AfricaFaculty of Sciences, King Abdulaziz University, Jeddah, Saudi ArabiaThe numerical approximation of the Caputo–Fabrizio fractional derivative with fractional order between 1 and 2 is proposed in this work. Using the transition from ordinary derivative to fractional derivative, we modified the RLC circuit model. The Crank–Nicolson numerical scheme was used to solve the modified model. We present the stability analysis of the numerical scheme for solving the modified equation and some numerical simulations for different values of the order of derivation.https://doi.org/10.1177/1687814015613758
collection DOAJ
language English
format Article
sources DOAJ
author Abdon Atangana
Juan Jose Nieto
spellingShingle Abdon Atangana
Juan Jose Nieto
Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
Advances in Mechanical Engineering
author_facet Abdon Atangana
Juan Jose Nieto
author_sort Abdon Atangana
title Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
title_short Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
title_full Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
title_fullStr Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
title_full_unstemmed Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel
title_sort numerical solution for the model of rlc circuit via the fractional derivative without singular kernel
publisher SAGE Publishing
series Advances in Mechanical Engineering
issn 1687-8140
publishDate 2015-10-01
description The numerical approximation of the Caputo–Fabrizio fractional derivative with fractional order between 1 and 2 is proposed in this work. Using the transition from ordinary derivative to fractional derivative, we modified the RLC circuit model. The Crank–Nicolson numerical scheme was used to solve the modified model. We present the stability analysis of the numerical scheme for solving the modified equation and some numerical simulations for different values of the order of derivation.
url https://doi.org/10.1177/1687814015613758
work_keys_str_mv AT abdonatangana numericalsolutionforthemodelofrlccircuitviathefractionalderivativewithoutsingularkernel
AT juanjosenieto numericalsolutionforthemodelofrlccircuitviathefractionalderivativewithoutsingularkernel
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