Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations
Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials. The left and right fractional differential expressions in Caputo sense...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/6036417 |
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| author | Haidong Qu Xiaopeng Yang Zihang She |
| author_facet | Haidong Qu Xiaopeng Yang Zihang She |
| author_sort | Haidong Qu |
| collection | DOAJ |
| description | Two new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials. The left and right fractional differential expressions in Caputo sense of the SFLPs are derived. As an application, it is effective for solving the fractional-order differential equations with the initial value problem by using the SFLP tau method. |
| format | Article |
| id | doaj-art-a2331e1e842747e696dbb9f418eea921 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-a2331e1e842747e696dbb9f418eea9212025-02-03T01:01:30ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/60364176036417Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential EquationsHaidong Qu0Xiaopeng Yang1Zihang She2Department of Mathematics, Hanshan Normal University, Chaozhou 521041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 521041, ChinaDepartment of Mathematics, Hanshan Normal University, Chaozhou 521041, ChinaTwo new orthogonal functions named the left- and the right-shifted fractional-order Legendre polynomials (SFLPs) are proposed. Several useful formulas for the SFLPs are directly generalized from the classic Legendre polynomials. The left and right fractional differential expressions in Caputo sense of the SFLPs are derived. As an application, it is effective for solving the fractional-order differential equations with the initial value problem by using the SFLP tau method.http://dx.doi.org/10.1155/2020/6036417 |
| spellingShingle | Haidong Qu Xiaopeng Yang Zihang She Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations Advances in Mathematical Physics |
| title | Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations |
| title_full | Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations |
| title_fullStr | Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations |
| title_full_unstemmed | Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations |
| title_short | Left- and Right-Shifted Fractional Legendre Functions with an Application for Fractional Differential Equations |
| title_sort | left and right shifted fractional legendre functions with an application for fractional differential equations |
| url | http://dx.doi.org/10.1155/2020/6036417 |
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