Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative
The present article introduces an operational approach based on modified hat functions to solve the space-time-fractional differential equations in the Caputo sense. In this method, the derivative of the unknown function is considered as a linear combination of modified hat functions. We use the ope...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2024-12-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_45556_340031334795eed9f0588de360ee0444.pdf |
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| author | E. Sedighi O. Baghani H. Azin |
| author_facet | E. Sedighi O. Baghani H. Azin |
| author_sort | E. Sedighi |
| collection | DOAJ |
| description | The present article introduces an operational approach based on modified hat functions to solve the space-time-fractional differential equations in the Caputo sense. In this method, the derivative of the unknown function is considered as a linear combination of modified hat functions. We use the operational matrix of the Riemann–Liouville fractional integral of modified hat functions to approximate the Caputo fractional derivative in order to reduce the problem to a system of Sylvester equations. The error of the mentioned method is of the order O(h3). In addition, we examine several numerical examples to confirm the ability of the proposed approach. |
| format | Article |
| id | doaj-art-6f61006f0cd24b518a8c951f8ce6cf62 |
| institution | OA Journals |
| issn | 2423-6977 2423-6969 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj-art-6f61006f0cd24b518a8c951f8ce6cf622025-08-20T02:21:02ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692024-12-0114Issue 41203122310.22067/ijnao.2024.87189.140545556Modified hat functions: Application in space-time-fractional differential equations with Caputo derivativeE. Sedighi0O. Baghani1H. Azin2Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Iran.Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Iran.Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Hakim Sabzevari University, Iran.The present article introduces an operational approach based on modified hat functions to solve the space-time-fractional differential equations in the Caputo sense. In this method, the derivative of the unknown function is considered as a linear combination of modified hat functions. We use the operational matrix of the Riemann–Liouville fractional integral of modified hat functions to approximate the Caputo fractional derivative in order to reduce the problem to a system of Sylvester equations. The error of the mentioned method is of the order O(h3). In addition, we examine several numerical examples to confirm the ability of the proposed approach.https://ijnao.um.ac.ir/article_45556_340031334795eed9f0588de360ee0444.pdfmodified hat functionsspace-time-fractional differential equationsoperational matrixcaputo fractional derivative |
| spellingShingle | E. Sedighi O. Baghani H. Azin Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative Iranian Journal of Numerical Analysis and Optimization modified hat functions space-time-fractional differential equations operational matrix caputo fractional derivative |
| title | Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative |
| title_full | Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative |
| title_fullStr | Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative |
| title_full_unstemmed | Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative |
| title_short | Modified hat functions: Application in space-time-fractional differential equations with Caputo derivative |
| title_sort | modified hat functions application in space time fractional differential equations with caputo derivative |
| topic | modified hat functions space-time-fractional differential equations operational matrix caputo fractional derivative |
| url | https://ijnao.um.ac.ir/article_45556_340031334795eed9f0588de360ee0444.pdf |
| work_keys_str_mv | AT esedighi modifiedhatfunctionsapplicationinspacetimefractionaldifferentialequationswithcaputoderivative AT obaghani modifiedhatfunctionsapplicationinspacetimefractionaldifferentialequationswithcaputoderivative AT hazin modifiedhatfunctionsapplicationinspacetimefractionaldifferentialequationswithcaputoderivative |