A New Method for Solving Sequential Fractional Wave Equations
In this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractio...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/5888010 |
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| _version_ | 1832554085437407232 |
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| author | Sondos M. Syam Z. Siri R. Md. Kasmani Kenan Yildirim |
| author_facet | Sondos M. Syam Z. Siri R. Md. Kasmani Kenan Yildirim |
| author_sort | Sondos M. Syam |
| collection | DOAJ |
| description | In this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractional wave equations. Due to the complexity of finding exact solutions for these problems, we employ a numerical technique based on the operational matrix method to approximate the solution. We provide several theoretical and numerical examples to validate the effectiveness of this numerical approach. The results demonstrate the accuracy and efficiency of the proposed method. |
| format | Article |
| id | doaj-art-61d02b71c1a34f06bd3066adf05d237f |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-61d02b71c1a34f06bd3066adf05d237f2025-02-03T05:52:24ZengWileyJournal of Mathematics2314-47852023-01-01202310.1155/2023/5888010A New Method for Solving Sequential Fractional Wave EquationsSondos M. Syam0Z. Siri1R. Md. Kasmani2Kenan Yildirim3Institute of Mathematical SciencesInstitute of Mathematical SciencesInstitute of Mathematical SciencesMus Alparslan UniversityIn this article, we focus on two classes of fractional wave equations in the context of the sequential Caputo derivative. For the first class, we derive the closed-form solution in terms of generalized Mittag–Leffler functions. Subsequently, we consider a more general class of nonhomogeneous fractional wave equations. Due to the complexity of finding exact solutions for these problems, we employ a numerical technique based on the operational matrix method to approximate the solution. We provide several theoretical and numerical examples to validate the effectiveness of this numerical approach. The results demonstrate the accuracy and efficiency of the proposed method.http://dx.doi.org/10.1155/2023/5888010 |
| spellingShingle | Sondos M. Syam Z. Siri R. Md. Kasmani Kenan Yildirim A New Method for Solving Sequential Fractional Wave Equations Journal of Mathematics |
| title | A New Method for Solving Sequential Fractional Wave Equations |
| title_full | A New Method for Solving Sequential Fractional Wave Equations |
| title_fullStr | A New Method for Solving Sequential Fractional Wave Equations |
| title_full_unstemmed | A New Method for Solving Sequential Fractional Wave Equations |
| title_short | A New Method for Solving Sequential Fractional Wave Equations |
| title_sort | new method for solving sequential fractional wave equations |
| url | http://dx.doi.org/10.1155/2023/5888010 |
| work_keys_str_mv | AT sondosmsyam anewmethodforsolvingsequentialfractionalwaveequations AT zsiri anewmethodforsolvingsequentialfractionalwaveequations AT rmdkasmani anewmethodforsolvingsequentialfractionalwaveequations AT kenanyildirim anewmethodforsolvingsequentialfractionalwaveequations AT sondosmsyam newmethodforsolvingsequentialfractionalwaveequations AT zsiri newmethodforsolvingsequentialfractionalwaveequations AT rmdkasmani newmethodforsolvingsequentialfractionalwaveequations AT kenanyildirim newmethodforsolvingsequentialfractionalwaveequations |