Solving Fractional Differential Equations by Using Triangle Neural Network
In this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The fractional derivative is considered Caputo type. The fractional derivative of the triangle neural network is analyzed first. Then, based on the technique of minimizing...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/5589905 |
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| _version_ | 1849684706395684864 |
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| author | Feng Gao Yumin Dong Chunmei Chi |
| author_facet | Feng Gao Yumin Dong Chunmei Chi |
| author_sort | Feng Gao |
| collection | DOAJ |
| description | In this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The fractional derivative is considered Caputo type. The fractional derivative of the triangle neural network is analyzed first. Then, based on the technique of minimizing the loss function of the neural network, the proposed numerical methods reduce the fractional differential equation into a gradient descent problem or the quadratic optimization problem. By using the gradient descent process or the quadratic optimization process, the numerical solution to the FDEs can be obtained. The efficiency and accuracy of the presented methods are shown by some numerical examples. Numerical tests show that this approach is easy to implement and accurate when applied to many types of FDEs. |
| format | Article |
| id | doaj-art-bad123188f8b4737a04bc7dab1b083c8 |
| institution | DOAJ |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-bad123188f8b4737a04bc7dab1b083c82025-08-20T03:23:23ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/55899055589905Solving Fractional Differential Equations by Using Triangle Neural NetworkFeng Gao0Yumin Dong1Chunmei Chi2School of Science, Qingdao University of Technology, Qingdao 266033, ChinaCollege of Computer and Information Science, Chongqing Normal University, Chongqing 401331, ChinaSchool of Information and Control Engineering, Qingdao University of Technology, Qingdao 266033, ChinaIn this paper, numerical methods for solving fractional differential equations by using a triangle neural network are proposed. The fractional derivative is considered Caputo type. The fractional derivative of the triangle neural network is analyzed first. Then, based on the technique of minimizing the loss function of the neural network, the proposed numerical methods reduce the fractional differential equation into a gradient descent problem or the quadratic optimization problem. By using the gradient descent process or the quadratic optimization process, the numerical solution to the FDEs can be obtained. The efficiency and accuracy of the presented methods are shown by some numerical examples. Numerical tests show that this approach is easy to implement and accurate when applied to many types of FDEs.http://dx.doi.org/10.1155/2021/5589905 |
| spellingShingle | Feng Gao Yumin Dong Chunmei Chi Solving Fractional Differential Equations by Using Triangle Neural Network Journal of Function Spaces |
| title | Solving Fractional Differential Equations by Using Triangle Neural Network |
| title_full | Solving Fractional Differential Equations by Using Triangle Neural Network |
| title_fullStr | Solving Fractional Differential Equations by Using Triangle Neural Network |
| title_full_unstemmed | Solving Fractional Differential Equations by Using Triangle Neural Network |
| title_short | Solving Fractional Differential Equations by Using Triangle Neural Network |
| title_sort | solving fractional differential equations by using triangle neural network |
| url | http://dx.doi.org/10.1155/2021/5589905 |
| work_keys_str_mv | AT fenggao solvingfractionaldifferentialequationsbyusingtriangleneuralnetwork AT yumindong solvingfractionaldifferentialequationsbyusingtriangleneuralnetwork AT chunmeichi solvingfractionaldifferentialequationsbyusingtriangleneuralnetwork |