An application of s-elementary wavelets in numerical solution of differential and fractional integral equations
In this article we introduce wavelet sets and consider a special wavelet set in R. We build a basis associated to this type wavelet sets and use operational matrix of this basis to solve nonlinear Riccati differential equations and Riemann-Liouville fractional integral equations of order $\alpha >...
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| Format: | Article |
| Language: | English |
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Shahid Bahonar University of Kerman
2022-11-01
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| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_3260_40b44a8692c0c11f8133b6e1700c3008.pdf |
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| _version_ | 1841556260787322880 |
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| author | Mohammad Javad Kheirdeh Ataollah Askari Hemmat Habibollah Saeedi |
| author_facet | Mohammad Javad Kheirdeh Ataollah Askari Hemmat Habibollah Saeedi |
| author_sort | Mohammad Javad Kheirdeh |
| collection | DOAJ |
| description | In this article we introduce wavelet sets and consider a special wavelet set in R. We build a basis associated to this type wavelet sets and use operational matrix of this basis to solve nonlinear Riccati differential equations and Riemann-Liouville fractional integral equations of order $\alpha >0$, numerically. Convergence analysis of this basis is investigated. Also, we give examples that show the accuracy of the new method by comparing it with previous methods. |
| format | Article |
| id | doaj-art-150fde986db3467dac688285c67d13b9 |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2022-11-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-150fde986db3467dac688285c67d13b92025-01-07T10:26:23ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052022-11-01113153110.22103/jmmrc.2022.18821.11933260An application of s-elementary wavelets in numerical solution of differential and fractional integral equationsMohammad Javad Kheirdeh0Ataollah Askari Hemmat1Habibollah Saeedi2Department of Mathematics, Payame Noor University (PNU) P. O. Box 19395-4697, Tehran, IranDepartment of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonal University of Kerman, Kerman, Iran.Department of Applied Mathematics, Faculty of Mathematics and Computer & Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, IranIn this article we introduce wavelet sets and consider a special wavelet set in R. We build a basis associated to this type wavelet sets and use operational matrix of this basis to solve nonlinear Riccati differential equations and Riemann-Liouville fractional integral equations of order $\alpha >0$, numerically. Convergence analysis of this basis is investigated. Also, we give examples that show the accuracy of the new method by comparing it with previous methods.https://jmmrc.uk.ac.ir/article_3260_40b44a8692c0c11f8133b6e1700c3008.pdfintegro-differential equationsfractional calculuswavelet setss-elementary wavelets |
| spellingShingle | Mohammad Javad Kheirdeh Ataollah Askari Hemmat Habibollah Saeedi An application of s-elementary wavelets in numerical solution of differential and fractional integral equations Journal of Mahani Mathematical Research integro-differential equations fractional calculus wavelet sets s-elementary wavelets |
| title | An application of s-elementary wavelets in numerical solution of differential and fractional integral equations |
| title_full | An application of s-elementary wavelets in numerical solution of differential and fractional integral equations |
| title_fullStr | An application of s-elementary wavelets in numerical solution of differential and fractional integral equations |
| title_full_unstemmed | An application of s-elementary wavelets in numerical solution of differential and fractional integral equations |
| title_short | An application of s-elementary wavelets in numerical solution of differential and fractional integral equations |
| title_sort | application of s elementary wavelets in numerical solution of differential and fractional integral equations |
| topic | integro-differential equations fractional calculus wavelet sets s-elementary wavelets |
| url | https://jmmrc.uk.ac.ir/article_3260_40b44a8692c0c11f8133b6e1700c3008.pdf |
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