Numerical solution of fractional differential equation by wavelets and hybrid functions
In this paper, we introduce methods based on operational matrix of fractional order integration for solving a typical n-term non-homogeneous fractional differential equation (FDE). We use Block pulse wavelets matrix of fractional order integration where a fractional derivative is defined in the Capu...
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2018-04-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/30904 |
| _version_ | 1797633460532150272 |
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| author | Amir Hosein Refahi Sheikhani Mahamad Mashoof |
| author_facet | Amir Hosein Refahi Sheikhani Mahamad Mashoof |
| author_sort | Amir Hosein Refahi Sheikhani |
| collection | DOAJ |
| description | In this paper, we introduce methods based on operational matrix of fractional order integration for solving a typical n-term non-homogeneous fractional differential equation (FDE). We use Block pulse wavelets matrix of fractional order integration where a fractional derivative is defined in the Caputo sense. Also we consider Hybrid of Block-pulse functions and shifted Legendre polynomials to approximate functions. By uses these methods we translate an FDE to an algebraic linear equations which can be solve. Methods has been tested by some numerical examples. |
| first_indexed | 2024-03-11T11:54:19Z |
| format | Article |
| id | doaj.art-dcbd342b06d3433588f985b8f4e9a7ab |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:54:19Z |
| publishDate | 2018-04-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-dcbd342b06d3433588f985b8f4e9a7ab2023-11-08T20:10:30ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882018-04-0136210.5269/bspm.v36i2.3090415446Numerical solution of fractional differential equation by wavelets and hybrid functionsAmir Hosein Refahi Sheikhani0Mahamad Mashoof1Islamic Azad UniversityIslamic Azad UniversityIn this paper, we introduce methods based on operational matrix of fractional order integration for solving a typical n-term non-homogeneous fractional differential equation (FDE). We use Block pulse wavelets matrix of fractional order integration where a fractional derivative is defined in the Caputo sense. Also we consider Hybrid of Block-pulse functions and shifted Legendre polynomials to approximate functions. By uses these methods we translate an FDE to an algebraic linear equations which can be solve. Methods has been tested by some numerical examples.https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/30904fractional order differential equationwaveletBlock pulseHybrid functionoperational matrices |
| spellingShingle | Amir Hosein Refahi Sheikhani Mahamad Mashoof Numerical solution of fractional differential equation by wavelets and hybrid functions Boletim da Sociedade Paranaense de Matemática fractional order differential equation wavelet Block pulse Hybrid function operational matrices |
| title | Numerical solution of fractional differential equation by wavelets and hybrid functions |
| title_full | Numerical solution of fractional differential equation by wavelets and hybrid functions |
| title_fullStr | Numerical solution of fractional differential equation by wavelets and hybrid functions |
| title_full_unstemmed | Numerical solution of fractional differential equation by wavelets and hybrid functions |
| title_short | Numerical solution of fractional differential equation by wavelets and hybrid functions |
| title_sort | numerical solution of fractional differential equation by wavelets and hybrid functions |
| topic | fractional order differential equation wavelet Block pulse Hybrid function operational matrices |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/30904 |
| work_keys_str_mv | AT amirhoseinrefahisheikhani numericalsolutionoffractionaldifferentialequationbywaveletsandhybridfunctions AT mahamadmashoof numericalsolutionoffractionaldifferentialequationbywaveletsandhybridfunctions |