Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations
We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the h...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/1535826 |
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| author | Yongjin Li Kamal Shah |
| author_facet | Yongjin Li Kamal Shah |
| author_sort | Yongjin Li |
| collection | DOAJ |
| description | We develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique. |
| format | Article |
| id | doaj-art-88166d4038f34c7da7fd4305992bb45b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-88166d4038f34c7da7fd4305992bb45b2025-08-20T03:37:44ZengWileyAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/15358261535826Numerical Solutions of Coupled Systems of Fractional Order Partial Differential EquationsYongjin Li0Kamal Shah1Department of Mathematics, Sun Yat-Sen University, Guangzhou, ChinaDepartment of Mathematics, University of Malakand, Chakdara Dir (L), Khyber Pakhtunkhwa, PakistanWe develop a numerical method by using operational matrices of fractional order integrations and differentiations to obtain approximate solutions to a class of coupled systems of fractional order partial differential equations (FPDEs). We use shifted Legendre polynomials in two variables. With the help of the aforesaid matrices, we convert the system under consideration to a system of easily solvable algebraic equation of Sylvester type. During this process, we need no discretization of the data. We also provide error analysis and some test problems to demonstrate the established technique.http://dx.doi.org/10.1155/2017/1535826 |
| spellingShingle | Yongjin Li Kamal Shah Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations Advances in Mathematical Physics |
| title | Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations |
| title_full | Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations |
| title_fullStr | Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations |
| title_full_unstemmed | Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations |
| title_short | Numerical Solutions of Coupled Systems of Fractional Order Partial Differential Equations |
| title_sort | numerical solutions of coupled systems of fractional order partial differential equations |
| url | http://dx.doi.org/10.1155/2017/1535826 |
| work_keys_str_mv | AT yongjinli numericalsolutionsofcoupledsystemsoffractionalorderpartialdifferentialequations AT kamalshah numericalsolutionsofcoupledsystemsoffractionalorderpartialdifferentialequations |