Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations
Abstract In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in o...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-03047-4 |
| _version_ | 1818529087939936256 |
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| author | Y. Yang M. H. Heydari Z. Avazzadeh A. Atangana |
| author_facet | Y. Yang M. H. Heydari Z. Avazzadeh A. Atangana |
| author_sort | Y. Yang |
| collection | DOAJ |
| description | Abstract In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in our method. In the established scheme, we approximate the unknown functions by CWs with unknown coefficients and reduce the problem to an algebraic system. In this way, we simplify the computation of nonlinear terms by obtaining some new results for CWs. Finally, we demonstrate the applicability of the presented algorithm by solving a few numerical examples. |
| first_indexed | 2024-12-11T06:58:33Z |
| format | Article |
| id | doaj.art-06f8b5e656b14360961c266e56c745ef |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T06:58:33Z |
| publishDate | 2020-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-06f8b5e656b14360961c266e56c745ef2022-12-22T01:16:40ZengSpringerOpenAdvances in Difference Equations1687-18472020-10-012020112410.1186/s13662-020-03047-4Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equationsY. Yang0M. H. Heydari1Z. Avazzadeh2A. Atangana3Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Hunan National Applied Mathematics Center, School of Mathematics and Computational Science, Xiangtan UniversityDepartment of Mathematics, Shiraz University of TechnologyFaculty of Mathematics and Statistics, Ton Duc Thang UniversityFaculty of Natural and Agricultural Sciences, University of the Free StateAbstract In this study, a wavelet method is developed to solve a system of nonlinear variable-order (V-O) fractional integral equations using the Chebyshev wavelets (CWs) and the Galerkin method. For this purpose, we derive a V-O fractional integration operational matrix (OM) for CWs and use it in our method. In the established scheme, we approximate the unknown functions by CWs with unknown coefficients and reduce the problem to an algebraic system. In this way, we simplify the computation of nonlinear terms by obtaining some new results for CWs. Finally, we demonstrate the applicability of the presented algorithm by solving a few numerical examples.http://link.springer.com/article/10.1186/s13662-020-03047-4Chebyshev wavelets (CWs)Variable-order (V-O) fractional integral equationsGalerkin methodOperational matrix (OM)Hat functions |
| spellingShingle | Y. Yang M. H. Heydari Z. Avazzadeh A. Atangana Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations Advances in Difference Equations Chebyshev wavelets (CWs) Variable-order (V-O) fractional integral equations Galerkin method Operational matrix (OM) Hat functions |
| title | Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations |
| title_full | Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations |
| title_fullStr | Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations |
| title_full_unstemmed | Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations |
| title_short | Chebyshev wavelets operational matrices for solving nonlinear variable-order fractional integral equations |
| title_sort | chebyshev wavelets operational matrices for solving nonlinear variable order fractional integral equations |
| topic | Chebyshev wavelets (CWs) Variable-order (V-O) fractional integral equations Galerkin method Operational matrix (OM) Hat functions |
| url | http://link.springer.com/article/10.1186/s13662-020-03047-4 |
| work_keys_str_mv | AT yyang chebyshevwaveletsoperationalmatricesforsolvingnonlinearvariableorderfractionalintegralequations AT mhheydari chebyshevwaveletsoperationalmatricesforsolvingnonlinearvariableorderfractionalintegralequations AT zavazzadeh chebyshevwaveletsoperationalmatricesforsolvingnonlinearvariableorderfractionalintegralequations AT aatangana chebyshevwaveletsoperationalmatricesforsolvingnonlinearvariableorderfractionalintegralequations |