Multi-step reproducing kernel algorithm for solving Caputo–Fabrizio fractional stiff models arising in electric circuits
Electrical engineering models can typically be simulated with a circuit of interconnected electrical components containing electrically charged particles that can be moved from atom to atom across a closed conducting pathway. In this paper, the electric circuit model of fractional stiff differential...
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| Vydáno v: | Soft computing (Berlin, Germany) Ročník 26; číslo 8; s. 3713 - 3727 |
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| Jazyk: | angličtina |
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Springer Berlin Heidelberg
01.04.2022
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| ISSN: | 1432-7643, 1433-7479 |
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| Abstract | Electrical engineering models can typically be simulated with a circuit of interconnected electrical components containing electrically charged particles that can be moved from atom to atom across a closed conducting pathway. In this paper, the electric circuit model of fractional stiff differential equations is investigated using a novel multi-step approach of reproducing kernel method (MS-RKM). Fractional operator with non-singular kernel, Caputo-Fabrizio fractional derivative, is considered to obtain accurate approximate solutions over a sequence of intervals for the fractional stiff system. To maintain dimensionality of the physical parameters appearing in the electrical circuit, a parameter is used to characterize the presence of fractional structures in the electrical model. Solving our model, in the context of classic numerical methods, is a difficult task, and solutions are often offered in a very small region with a very slow rate of convergence or they may diverge in wider regions. MS-RKM is treated as a new modification of RKM on subintervals, which considerably reduces the number of arithmetic operations and thus time and effort to get approximate solutions. Efficiency, simplicity, and accuracy of the proposed multi-step approach in solving the fractional stiff system is evident through numerical simulations performed for RL, RC, and RLC circuit models. |
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| AbstractList | Electrical engineering models can typically be simulated with a circuit of interconnected electrical components containing electrically charged particles that can be moved from atom to atom across a closed conducting pathway. In this paper, the electric circuit model of fractional stiff differential equations is investigated using a novel multi-step approach of reproducing kernel method (MS-RKM). Fractional operator with non-singular kernel, Caputo-Fabrizio fractional derivative, is considered to obtain accurate approximate solutions over a sequence of intervals for the fractional stiff system. To maintain dimensionality of the physical parameters appearing in the electrical circuit, a parameter is used to characterize the presence of fractional structures in the electrical model. Solving our model, in the context of classic numerical methods, is a difficult task, and solutions are often offered in a very small region with a very slow rate of convergence or they may diverge in wider regions. MS-RKM is treated as a new modification of RKM on subintervals, which considerably reduces the number of arithmetic operations and thus time and effort to get approximate solutions. Efficiency, simplicity, and accuracy of the proposed multi-step approach in solving the fractional stiff system is evident through numerical simulations performed for RL, RC, and RLC circuit models. |
| Author | Dutta, Hemen Hasan, Shatha Momani, Shaher Hadid, Samir Al-Smadi, Mohammed |
| Author_xml | – sequence: 1 givenname: Shatha surname: Hasan fullname: Hasan, Shatha organization: Department of Applied Science, Ajloun College, Al-Balqa Applied University – sequence: 2 givenname: Mohammed surname: Al-Smadi fullname: Al-Smadi, Mohammed organization: Department of Applied Science, Ajloun College, Al-Balqa Applied University, College of Commerce and Business, Lusail University, Nonlinear Dynamics Research Center (NDRC), Ajman University – sequence: 3 givenname: Hemen surname: Dutta fullname: Dutta, Hemen email: duttah@gauhati.ac.in organization: Department of Mathematics, Gauhati University – sequence: 4 givenname: Shaher surname: Momani fullname: Momani, Shaher organization: Nonlinear Dynamics Research Center (NDRC), Ajman University, Department of Mathematics, Faculty of Science, The University of Jordan – sequence: 5 givenname: Samir surname: Hadid fullname: Hadid, Samir organization: Nonlinear Dynamics Research Center (NDRC), Ajman University |
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| Cites_doi | 10.1016/j.chaos.2020.109624 10.1016/j.aml.2011.03.032 10.1007/978-3-030-45355-8 10.1186/s13662-019-2042-3 10.1016/j.jnnms.2016.02.002 10.1186/s13662-019-1996-5 10.1016/j.amc.2016.06.002 10.1073/pnas.38.3.235 10.1016/S1405-7743(14)72219-X 10.1051/mmnp/2021030 10.1016/j.chaos.2020.110506 10.1016/j.procs.2017.12.063 10.1016/j.chaos.2021.110891 10.1016/j.jnnms.2015.06.002 10.1016/j.physa.2019.123257 10.4236/am.2013.43065 10.1088/1402-4896/ab96e0 |
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| Keywords | Reproducing kernel method Caputo–Fabrizio fractional derivative Multi-step approach Electrical circuits Stiff system |
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| References | Al-Smadi, Abu Arqub, Shawagfeh, Momani (CR4) 2016; 291 Idrees, Mabood, Ali, Zaman (CR21) 2013; 4 Caputo, Fabrizio (CR12) 2015; 1 Akinfenwa, Akinnukawe, Mudasiru (CR2) 2015; 34 Hasan, Al-Smadi, Freihet, Momani (CR18) 2019; 2019 Freihet, Hasan, Al-Smadi, Gaith, Momani (CR15) 2019; 2019 Kanth, Garg (CR22) 2018; 125 Kilbas, Srivastava, Trujillo (CR23) 2006 CR13 Al-Smadi, Abu Arqub, Zeidan (CR7) 2021; 146 Losada, Nieto (CR25) 2015; 1 Al-Smadi, Freihat, Khalil, Momani, Khan (CR5) 2017; 14 Al-Smadi, Dutta, Hasan, Momani (CR8) 2021; 16 Hasan, El-Ajou, Hadid, Al-Smadi, Momani (CR19) 2020; 133 Hasan, Al-Smadi, El-Ajou, Momani, Hadid, Al-Zhour (CR20) 2021; 143 Gómez-Aguilar, Razo-Hernández, Rosales-García, Guía-Calderón (CR17) 2014; 15 Atay, Kilic (CR11) 2013; 143915 Abu Arqub, Al-Smadi (CR1) 2020; 540 Al-Smadi, Abu Arqub, Momani (CR6) 2020; 95 Al-Smadi, Abu Arqub (CR3) 2019; 342 Curtiss, Hirschfelder (CR14) 1952; 38 Atangana (CR10) 2016; 273 Aminikhah, Hemmatnezhad (CR9) 2011; 24 Yakubu, Markus (CR29) 2016; 35 Miller, Ross (CR26) 1993 Gómez-Aguilar, Rosales-García, Bernal-Alvarado, Córdova-Fraga, Guzmán-Cabrera (CR16) 2012; 58 Li, Cui (CR24) 2003; 143 Oldham, Spanier (CR27) 1974 Senthil Kumar, Dutta (CR28) 2020 JF Gómez-Aguilar (6885_CR16) 2012; 58 M Al-Smadi (6885_CR5) 2017; 14 JF Gómez-Aguilar (6885_CR17) 2014; 15 BV Senthil Kumar (6885_CR28) 2020 6885_CR13 O Abu Arqub (6885_CR1) 2020; 540 M Idrees (6885_CR21) 2013; 4 S Hasan (6885_CR19) 2020; 133 M Al-Smadi (6885_CR4) 2016; 291 A Atangana (6885_CR10) 2016; 273 M Atay (6885_CR11) 2013; 143915 A Freihet (6885_CR15) 2019; 2019 D Yakubu (6885_CR29) 2016; 35 S Hasan (6885_CR18) 2019; 2019 K Miller (6885_CR26) 1993 AR Kanth (6885_CR22) 2018; 125 M Al-Smadi (6885_CR6) 2020; 95 O Akinfenwa (6885_CR2) 2015; 34 M Al-Smadi (6885_CR3) 2019; 342 K Oldham (6885_CR27) 1974 S Hasan (6885_CR20) 2021; 143 M Al-Smadi (6885_CR7) 2021; 146 A Kilbas (6885_CR23) 2006 M Caputo (6885_CR12) 2015; 1 C Curtiss (6885_CR14) 1952; 38 M Al-Smadi (6885_CR8) 2021; 16 J Losada (6885_CR25) 2015; 1 C Li (6885_CR24) 2003; 143 H Aminikhah (6885_CR9) 2011; 24 |
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| Title | Multi-step reproducing kernel algorithm for solving Caputo–Fabrizio fractional stiff models arising in electric circuits |
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