Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation
Abstract In this paper, we give an analytical solution of a fractional wave equation for a vibrating string with Caputo time fractional derivatives. We obtain the exact solution in terms of three parameter Mittag-Leffler function. Furthermore, some examples of the main result are exhibited.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2110-8 |
| _version_ | 1818238989357809664 |
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| author | Mehmet Ali Özarslan Cemaliye Kürt |
| author_facet | Mehmet Ali Özarslan Cemaliye Kürt |
| author_sort | Mehmet Ali Özarslan |
| collection | DOAJ |
| description | Abstract In this paper, we give an analytical solution of a fractional wave equation for a vibrating string with Caputo time fractional derivatives. We obtain the exact solution in terms of three parameter Mittag-Leffler function. Furthermore, some examples of the main result are exhibited. |
| first_indexed | 2024-12-12T12:50:25Z |
| format | Article |
| id | doaj.art-41813ee2e5be4da88881ef8944e44fe0 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-12T12:50:25Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-41813ee2e5be4da88881ef8944e44fe02022-12-22T00:24:01ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019111410.1186/s13662-019-2110-8Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equationMehmet Ali Özarslan0Cemaliye Kürt1Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean UniversityDepartment of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean UniversityAbstract In this paper, we give an analytical solution of a fractional wave equation for a vibrating string with Caputo time fractional derivatives. We obtain the exact solution in terms of three parameter Mittag-Leffler function. Furthermore, some examples of the main result are exhibited.http://link.springer.com/article/10.1186/s13662-019-2110-8Fractional wave equationCaputo time fractional derivativeMittag-Leffler functionLaplace transform |
| spellingShingle | Mehmet Ali Özarslan Cemaliye Kürt Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation Advances in Difference Equations Fractional wave equation Caputo time fractional derivative Mittag-Leffler function Laplace transform |
| title | Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation |
| title_full | Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation |
| title_fullStr | Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation |
| title_full_unstemmed | Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation |
| title_short | Nonhomogeneous initial and boundary value problem for the Caputo-type fractional wave equation |
| title_sort | nonhomogeneous initial and boundary value problem for the caputo type fractional wave equation |
| topic | Fractional wave equation Caputo time fractional derivative Mittag-Leffler function Laplace transform |
| url | http://link.springer.com/article/10.1186/s13662-019-2110-8 |
| work_keys_str_mv | AT mehmetaliozarslan nonhomogeneousinitialandboundaryvalueproblemforthecaputotypefractionalwaveequation AT cemaliyekurt nonhomogeneousinitialandboundaryvalueproblemforthecaputotypefractionalwaveequation |