A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations
In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial. First, we derived the operational matrices for integer and fractional order derivatives. Then, usin...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2021-08-01
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| Series: | Alexandria Engineering Journal |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682100082X |
| _version_ | 1818663130625998848 |
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| author | Jumana H.S. Alkhalissi Ibrahim Emiroglu Mustafa Bayram Aydin Secer Fatih Tasci |
| author_facet | Jumana H.S. Alkhalissi Ibrahim Emiroglu Mustafa Bayram Aydin Secer Fatih Tasci |
| author_sort | Jumana H.S. Alkhalissi |
| collection | DOAJ |
| description | In this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial. First, we derived the operational matrices for integer and fractional order derivatives. Then, using these operational matrices with the proposed method, we transformed the given problem into a system of algebraic equations. Then, some linear and nonlinear examples were considered and discussed to confirm the efficiency and accuracy of the proposed method. |
| first_indexed | 2024-12-17T05:11:57Z |
| format | Article |
| id | doaj.art-d360d91a07d44ffa8f4ad67d7cb9b759 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-17T05:11:57Z |
| publishDate | 2021-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-d360d91a07d44ffa8f4ad67d7cb9b7592022-12-21T22:02:15ZengElsevierAlexandria Engineering Journal1110-01682021-08-0160435093519A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equationsJumana H.S. Alkhalissi0Ibrahim Emiroglu1Mustafa Bayram2Aydin Secer3Fatih Tasci4Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey; Corresponding author.Department of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyDepartment of Computer Engineering, Biruni University, Istanbul, TurkeyDepartment of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyDepartment of Mathematical Engineering, Yildiz Technical University, Istanbul, TurkeyIn this paper, a new type of wavelet method to solve fractional differential equations (linear or nonlinear) is proposed. The proposed method is based on the generalized Gegenbauer–Humbert polynomial. First, we derived the operational matrices for integer and fractional order derivatives. Then, using these operational matrices with the proposed method, we transformed the given problem into a system of algebraic equations. Then, some linear and nonlinear examples were considered and discussed to confirm the efficiency and accuracy of the proposed method.http://www.sciencedirect.com/science/article/pii/S111001682100082X00-0199-00 |
| spellingShingle | Jumana H.S. Alkhalissi Ibrahim Emiroglu Mustafa Bayram Aydin Secer Fatih Tasci A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations Alexandria Engineering Journal 00-01 99-00 |
| title | A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations |
| title_full | A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations |
| title_fullStr | A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations |
| title_full_unstemmed | A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations |
| title_short | A new operational matrix of fractional derivative based on the generalized Gegenbauer–Humbert polynomials to solve fractional differential equations |
| title_sort | new operational matrix of fractional derivative based on the generalized gegenbauer humbert polynomials to solve fractional differential equations |
| topic | 00-01 99-00 |
| url | http://www.sciencedirect.com/science/article/pii/S111001682100082X |
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