Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks
This study aims to employ artificial neural networks (ANNs) as a novel method for solving time fractional telegraph equations (TFTEs), which are typically addressed using the Caputo fractional derivative in scientific investigations. By integrating Chebyshev polynomials as a substitute for the tradi...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute of Physics
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/114374/ http://psasir.upm.edu.my/id/eprint/114374/1/114374.pdf |
| _version_ | 1848866474621403136 |
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| author | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali |
| author_facet | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali |
| author_sort | Ali, Amina Hassan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This study aims to employ artificial neural networks (ANNs) as a novel method for solving time fractional telegraph equations (TFTEs), which are typically addressed using the Caputo fractional derivative in scientific investigations. By integrating Chebyshev polynomials as a substitute for the traditional hidden layer, computational performance is enhanced, and the range of input patterns is broadened. A feed-forward neural network (NN) model, optimized using the adaptive moment estimation (Adam) technique, is utilized to refine network parameters and minimize errors. Additionally, the Taylor series is applied to the activation function, which removes any limitation on taking fractional derivatives during the minimization process. Several benchmark problems are selected to evaluate the proposed method, and their numerical solutions are obtained. The results demonstrate the method’s effectiveness and accuracy, as evidenced by the close agreement between the numerical solutions and analytical solutions. |
| first_indexed | 2025-11-15T14:21:11Z |
| format | Article |
| id | upm-114374 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:21:11Z |
| publishDate | 2024 |
| publisher | Institute of Physics |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1143742025-01-20T00:50:14Z http://psasir.upm.edu.my/id/eprint/114374/ Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks Ali, Amina Hassan Senu, Norazak Ahmadian, Ali This study aims to employ artificial neural networks (ANNs) as a novel method for solving time fractional telegraph equations (TFTEs), which are typically addressed using the Caputo fractional derivative in scientific investigations. By integrating Chebyshev polynomials as a substitute for the traditional hidden layer, computational performance is enhanced, and the range of input patterns is broadened. A feed-forward neural network (NN) model, optimized using the adaptive moment estimation (Adam) technique, is utilized to refine network parameters and minimize errors. Additionally, the Taylor series is applied to the activation function, which removes any limitation on taking fractional derivatives during the minimization process. Several benchmark problems are selected to evaluate the proposed method, and their numerical solutions are obtained. The results demonstrate the method’s effectiveness and accuracy, as evidenced by the close agreement between the numerical solutions and analytical solutions. Institute of Physics 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/114374/1/114374.pdf Ali, Amina Hassan and Senu, Norazak and Ahmadian, Ali (2024) Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks. Physica Scripta, 99 (11). art. no. 115210. ISSN 0031-8949; eISSN: 1402-4896 (In Press) https://iopscience.iop.org/article/10.1088/1402-4896/ad7c93 10.1088/1402-4896/ad7c93 |
| spellingShingle | Ali, Amina Hassan Senu, Norazak Ahmadian, Ali Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title | Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title_full | Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title_fullStr | Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title_full_unstemmed | Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title_short | Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks |
| title_sort | efficient solutions to time-fractional telegraph equations with chebyshev neural networks |
| url | http://psasir.upm.edu.my/id/eprint/114374/ http://psasir.upm.edu.my/id/eprint/114374/ http://psasir.upm.edu.my/id/eprint/114374/ http://psasir.upm.edu.my/id/eprint/114374/1/114374.pdf |