On the Solutions of a Class of Discrete PWC Systems Modeled with Caputo-Type Delta Fractional Difference Equations
In this paper, it is shown that a class of discrete Piece Wise Continuous (PWC) systems with Caputo-type delta fractional difference may not have solutions. To overcome this obstacle, the discontinuous problem is restarted as a continuous fractional problem. First, the single-valued PWC problem is t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/7/4/304 |
| Summary: | In this paper, it is shown that a class of discrete Piece Wise Continuous (PWC) systems with Caputo-type delta fractional difference may not have solutions. To overcome this obstacle, the discontinuous problem is restarted as a continuous fractional problem. First, the single-valued PWC problem is transformed into a set-valued one via Filippov’s theory, after which Cellina’s theorem allows the restart of the problem into a single-valued continuous one. A numerical example is proposed and analyzed. |
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| ISSN: | 2504-3110 |