Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems
In this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractionalorder systems, which...
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World Scientific
2025
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| Online Access: | http://eprints.uthm.edu.my/12727/1/J19696_8ff506a5cb4f6606cdbd7debde056937.pdf http://eprints.uthm.edu.my/12727/ https://doi.org/10.1142/S0218126625500951 |
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| author | Ibrahim, Salisu Isah, Abdulnasir Iqbal, Mujahid Chang, Phang Baleanu, Dumitru |
| author_facet | Ibrahim, Salisu Isah, Abdulnasir Iqbal, Mujahid Chang, Phang Baleanu, Dumitru |
| author_sort | Ibrahim, Salisu |
| building | UTHM Library |
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| content_provider | Universiti Tun Hussein Onn Malaysia |
| content_source | UTHM Institutional Repository |
| continent | Asia |
| country | Malaysia |
| description | In this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractionalorder systems, which are characterized by a noninteger-order derivative, have been widely
studied in recent years due to their ability to model a wide range of phenomena. However, the commutativity of fractional-order LTVSs has not been widely explored. In this work, we present a comprehensive study of the commutativity of fractional-order LTVSs. We ¯rst provide a mathematical de¯nition of commutativity for these systems and demonstrate that it is equivalent to the commutativity of their transfer functions. We then propose a method for verifying the general condition for commutativity of fractional-order LTVSs under zero initial conditions (ICs) and prove it mathematically. Based on our ¯ndings, we realized that the commutative requirements, properties, theories, and conditions are general for fractional-order LTVSs, please observed that some fractional-order LTVSs are commutative, some are not commutative, while
some are commutative under certain conditions. Based on this fact, we can say that not all fractional-order LTVSs are commutative. We apply explicit commutative results to several examples of fractional-order LTVSs. Our
theoretical and simulation results show a good agreement and prove that our fractional-order LTVSs are commutative under certain conditions, moreover, the commutativity property holds for certain conditions and classes of fractional-order LTVSs, but not for others. Because of the application of fraction commutativity in various ¯elds of science and engineering, we ¯nd it necessary to come up with explicit results for the ¯rst time. |
| format | Article |
| id | my.uthm.eprints-12727 |
| institution | Universiti Tun Hussein Onn Malaysia |
| language | en |
| publishDate | 2025 |
| publisher | World Scientific |
| record_format | eprints |
| spelling | my.uthm.eprints-127272025-06-26T00:07:47Z http://eprints.uthm.edu.my/12727/ Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems Ibrahim, Salisu Isah, Abdulnasir Iqbal, Mujahid Chang, Phang Baleanu, Dumitru Q Science (General) QA Mathematics In this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractionalorder systems, which are characterized by a noninteger-order derivative, have been widely studied in recent years due to their ability to model a wide range of phenomena. However, the commutativity of fractional-order LTVSs has not been widely explored. In this work, we present a comprehensive study of the commutativity of fractional-order LTVSs. We ¯rst provide a mathematical de¯nition of commutativity for these systems and demonstrate that it is equivalent to the commutativity of their transfer functions. We then propose a method for verifying the general condition for commutativity of fractional-order LTVSs under zero initial conditions (ICs) and prove it mathematically. Based on our ¯ndings, we realized that the commutative requirements, properties, theories, and conditions are general for fractional-order LTVSs, please observed that some fractional-order LTVSs are commutative, some are not commutative, while some are commutative under certain conditions. Based on this fact, we can say that not all fractional-order LTVSs are commutative. We apply explicit commutative results to several examples of fractional-order LTVSs. Our theoretical and simulation results show a good agreement and prove that our fractional-order LTVSs are commutative under certain conditions, moreover, the commutativity property holds for certain conditions and classes of fractional-order LTVSs, but not for others. Because of the application of fraction commutativity in various ¯elds of science and engineering, we ¯nd it necessary to come up with explicit results for the ¯rst time. World Scientific 2025 Article PeerReviewed text en http://eprints.uthm.edu.my/12727/1/J19696_8ff506a5cb4f6606cdbd7debde056937.pdf Ibrahim, Salisu and Isah, Abdulnasir and Iqbal, Mujahid and Chang, Phang and Baleanu, Dumitru (2025) Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems. Journal of Circuits, Systems, and Computers, 34 (4). pp. 1-14. https://doi.org/10.1142/S0218126625500951 |
| spellingShingle | Q Science (General) QA Mathematics Ibrahim, Salisu Isah, Abdulnasir Iqbal, Mujahid Chang, Phang Baleanu, Dumitru Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title | Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title_full | Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title_fullStr | Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title_full_unstemmed | Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title_short | Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems |
| title_sort | commutativity of cascaded connected fractional order linear time-varying systems |
| topic | Q Science (General) QA Mathematics |
| url | http://eprints.uthm.edu.my/12727/1/J19696_8ff506a5cb4f6606cdbd7debde056937.pdf http://eprints.uthm.edu.my/12727/ https://doi.org/10.1142/S0218126625500951 |
| url_provider | http://eprints.uthm.edu.my/ |