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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| Published in | Advances in mechanical engineering Vol. 7; no. 10; p. 1 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
London, England
SAGE Publications
01.10.2015
Sage Publications Ltd SAGE Publishing |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Atangana, Abdon Nieto, Juan Jose |
| Author_xml | – sequence: 1 givenname: Abdon surname: Atangana fullname: Atangana, Abdon email: abdonatangana@yahoo.fr – sequence: 2 givenname: Juan Jose surname: Nieto fullname: Nieto, Juan Jose |
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| Cites_doi | 10.1016/S0304-0208(06)80001-0 10.1155/2013/279681 10.1177/1077546307087439 10.1002/cta.353 10.1007/s00521-014-1586-0 |
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| Keywords | RLC circuit numerical approximation stability analysis Fractional derivative without singular kernel |
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| References | Caputo, Fabrizio 2015; 1 Riaza 2006; 34 Losada, Nieto 2015; 1 Magin, Ovadia 2008; 14 Cloot, Botha 2006; 32 Atangana, Alkatani 2015; 7 Podlubny 2002; 5 Atangana, Secer 2013; 2013 Atangana 2014; 25 Podlubny I (bibr3-1687814015613758) 2002; 5 Kilbas AA (bibr2-1687814015613758) 2006; 204 bibr6-1687814015613758 Losada J (bibr8-1687814015613758) 2015; 1 bibr5-1687814015613758 Atangana A (bibr9-1687814015613758) 2015; 7 bibr10-1687814015613758 bibr1-1687814015613758 Cloot A (bibr4-1687814015613758) 2006; 32 Caputo M (bibr7-1687814015613758) 2015; 1 |
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| Title | Numerical solution for the model of RLC circuit via the fractional derivative without singular kernel |
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