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.
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Abstract
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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | Fractional di®erential equation; commutativity; physical systems; equivalent circuit; signal processing; sensitivity; analog control. |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Center for Diploma Studies > Dept. of Science and Mathematics |
| Depositing User: | Mr. Mohamad Zulkhibri Rahmad |
| Date Deposited: | 26 Jun 2025 00:07 |
| Last Modified: | 26 Jun 2025 00:07 |
| URI: | http://eprints.uthm.edu.my/id/eprint/12727 |
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