A Numerical Method for Solving Fractional Differential Equations by Using Neural Network
We present a new method for solving the fractional differential equations of initial value problems by using neural networks which are constructed from cosine basis functions with adjustable parameters. By training the neural networks repeatedly the numerical solutions for the fractional differentia...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2015-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2015/439526 |
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doaj-bdd167c16687455ebeb3e01bbbcfaa8e2021-07-02T02:56:35ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392015-01-01201510.1155/2015/439526439526A Numerical Method for Solving Fractional Differential Equations by Using Neural NetworkHaidong Qu0Xuan Liu1Department of Mathematics, Hanshan Normal University, Chaozhou 521041, ChinaDepartment of Basic Education, Hanshan Normal University, Chaozhou 521041, ChinaWe present a new method for solving the fractional differential equations of initial value problems by using neural networks which are constructed from cosine basis functions with adjustable parameters. By training the neural networks repeatedly the numerical solutions for the fractional differential equations were obtained. Moreover, the technique is still applicable for the coupled differential equations of fractional order. The computer graphics and numerical solutions show that the proposed method is very effective.http://dx.doi.org/10.1155/2015/439526 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Haidong Qu Xuan Liu |
| spellingShingle |
Haidong Qu Xuan Liu A Numerical Method for Solving Fractional Differential Equations by Using Neural Network Advances in Mathematical Physics |
| author_facet |
Haidong Qu Xuan Liu |
| author_sort |
Haidong Qu |
| title |
A Numerical Method for Solving Fractional Differential Equations by Using Neural Network |
| title_short |
A Numerical Method for Solving Fractional Differential Equations by Using Neural Network |
| title_full |
A Numerical Method for Solving Fractional Differential Equations by Using Neural Network |
| title_fullStr |
A Numerical Method for Solving Fractional Differential Equations by Using Neural Network |
| title_full_unstemmed |
A Numerical Method for Solving Fractional Differential Equations by Using Neural Network |
| title_sort |
numerical method for solving fractional differential equations by using neural network |
| publisher |
Hindawi Limited |
| series |
Advances in Mathematical Physics |
| issn |
1687-9120 1687-9139 |
| publishDate |
2015-01-01 |
| description |
We present a new method for solving the fractional differential equations
of initial value problems by using neural networks which are constructed from
cosine basis functions with adjustable parameters. By training the neural networks
repeatedly the numerical solutions for the fractional differential equations were
obtained. Moreover, the technique is still applicable for the coupled differential equations
of fractional order. The computer graphics and numerical solutions show
that the proposed method is very effective. |
| url |
http://dx.doi.org/10.1155/2015/439526 |
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1721342598933643264 |