Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels
In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integrat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2023-09-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_43722_e854731ae97a2dfa19bca6976f0d1067.pdf |
| _version_ | 1827895475345293312 |
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| author | H. Ebrahimi J. Biazar |
| author_facet | H. Ebrahimi J. Biazar |
| author_sort | H. Ebrahimi |
| collection | DOAJ |
| description | In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures. |
| first_indexed | 2024-03-12T22:21:28Z |
| format | Article |
| id | doaj.art-20476ea5f2f0492db09d6dfbf279170b |
| institution | Directory Open Access Journal |
| issn | 2423-6977 2423-6969 |
| language | English |
| last_indexed | 2024-03-12T22:21:28Z |
| publishDate | 2023-09-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj.art-20476ea5f2f0492db09d6dfbf279170b2023-07-23T05:04:02ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692023-09-0113350053110.22067/ijnao.2023.80249.120943722Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernelsH. Ebrahimi0J. Biazar1Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.In the current study, a new numerical algorithm is presented to solve a class of nonlinear fractional integral-differential equations with weakly singular kernels. Cubic hat functions (CHFs) and their properties are introduced for the first time. A new fractional-order operational matrix of integration via CHFs is presented. Utilizing the operational matrices of CHFs, the main problem is transformed into a number of trivariate polynomial equations. Error analysis and the convergence of the proposed method are evaluated, and the convergence rate is addressed. Ultimately, three examples are provided to illustrate the precision and capabilities of this algorithm. The numerical results are presented in some tables and figures.https://ijnao.um.ac.ir/article_43722_e854731ae97a2dfa19bca6976f0d1067.pdffractional integral-differential equationsnumerical algorithmsweakly singular kernelscubic hat functionsfractional operational matrix |
| spellingShingle | H. Ebrahimi J. Biazar Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels Iranian Journal of Numerical Analysis and Optimization fractional integral-differential equations numerical algorithms weakly singular kernels cubic hat functions fractional operational matrix |
| title | Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels |
| title_full | Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels |
| title_fullStr | Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels |
| title_full_unstemmed | Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels |
| title_short | Cubic hat-functions approximation for linear and nonlinear fractional integral-differential equations with weakly singular kernels |
| title_sort | cubic hat functions approximation for linear and nonlinear fractional integral differential equations with weakly singular kernels |
| topic | fractional integral-differential equations numerical algorithms weakly singular kernels cubic hat functions fractional operational matrix |
| url | https://ijnao.um.ac.ir/article_43722_e854731ae97a2dfa19bca6976f0d1067.pdf |
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