The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative
Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time. With help of the law of switch and the Kirchhoff Voltage Laws, the transien...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-12-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016820304129 |
| _version_ | 1823941536319012864 |
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| author | Kang-Jia Wang Hong-Chang Sun Zhe Fei |
| author_facet | Kang-Jia Wang Hong-Chang Sun Zhe Fei |
| author_sort | Kang-Jia Wang |
| collection | DOAJ |
| description | Local fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time. With help of the law of switch and the Kirchhoff Voltage Laws, the transient local fractional ordinary differential equation is established, and the corresponding exact solution behavior defined on Cantor sets is presented. What we found especially interesting was that the fractal RC becomes the ordinary one in the particular case κ = 1. The results obtained in this paper reveal that the local fractional calculus is a powerful tool to analyze the fractal circuit systems. |
| first_indexed | 2024-12-17T04:28:33Z |
| format | Article |
| id | doaj.art-75e55ad618db4d8295db021d98502e8c |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-17T04:28:33Z |
| publishDate | 2020-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-75e55ad618db4d8295db021d98502e8c2022-12-21T22:03:38ZengElsevierAlexandria Engineering Journal1110-01682020-12-0159646694675The transient analysis for zero-input response of fractal RC circuit based on local fractional derivativeKang-Jia Wang0Hong-Chang Sun1Zhe Fei2School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo 454003, ChinaSchool of Control Science and Engineering, Shandong University, Jinan 250061, China; Shandong Dawei International Architecture Design Co., Ltd., Jinan 250101, China; Corresponding author at: School of Control Science and Engineering, Shandong University, Jinan 250061, China and Shandong Dawei International Architecture Design Co., Ltd., Jinan 250101, China.Shandong Dawei International Architecture Design Co., Ltd., Jinan 250101, ChinaLocal fractional calculus has gained wide attention in the field of circuit design. In this paper, we propose the zero-input response(ZIR) of fractal RC circuit modeled by local fractional derivative(LFD) for the first time. With help of the law of switch and the Kirchhoff Voltage Laws, the transient local fractional ordinary differential equation is established, and the corresponding exact solution behavior defined on Cantor sets is presented. What we found especially interesting was that the fractal RC becomes the ordinary one in the particular case κ = 1. The results obtained in this paper reveal that the local fractional calculus is a powerful tool to analyze the fractal circuit systems.http://www.sciencedirect.com/science/article/pii/S1110016820304129Local fractional calculusLocal fractional derivativeZero-input responseFractal circuit systems |
| spellingShingle | Kang-Jia Wang Hong-Chang Sun Zhe Fei The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative Alexandria Engineering Journal Local fractional calculus Local fractional derivative Zero-input response Fractal circuit systems |
| title | The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative |
| title_full | The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative |
| title_fullStr | The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative |
| title_full_unstemmed | The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative |
| title_short | The transient analysis for zero-input response of fractal RC circuit based on local fractional derivative |
| title_sort | transient analysis for zero input response of fractal rc circuit based on local fractional derivative |
| topic | Local fractional calculus Local fractional derivative Zero-input response Fractal circuit systems |
| url | http://www.sciencedirect.com/science/article/pii/S1110016820304129 |
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