An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks
This study aims to develop a new strategy for solving partial differential equations with fractional derivatives (FPDEs) using artificial neural networks (ANNs). Numerical solutions to FPDEs are obtained through the Hermite wavelet neural network (HWNN) model. The Caputo fractional derivative is con...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2024
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| Online Access: | http://psasir.upm.edu.my/id/eprint/116395/ http://psasir.upm.edu.my/id/eprint/116395/1/116395%20v2.pdf |
| _version_ | 1848866994284134400 |
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| author | Ali, Amina Senu, Norazak Wahi, Nadihah Almakayeel, Naif Ahmadian, Ali |
| author_facet | Ali, Amina Senu, Norazak Wahi, Nadihah Almakayeel, Naif Ahmadian, Ali |
| author_sort | Ali, Amina |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This study aims to develop a new strategy for solving partial differential equations with fractional derivatives (FPDEs) using artificial neural networks (ANNs). Numerical solutions to FPDEs are obtained through the Hermite wavelet neural network (HWNN) model. The Caputo fractional derivative is consistently applied throughout the research to address fractional-order partial differential problems. To enhance computational efficiency and expand the input pattern, the hidden layer is removed. A neural network (NN) model featuring a feed-forward architecture and error-back propagation without supervision is employed to optimize network parameters and minimize errors. Numerical illustrations are presented to demonstrate the effectiveness of this approach in preserving computational efficiency while solving FPDEs. |
| first_indexed | 2025-11-15T14:29:26Z |
| format | Article |
| id | upm-116395 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T14:29:26Z |
| publishDate | 2024 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1163952025-04-10T06:48:25Z http://psasir.upm.edu.my/id/eprint/116395/ An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks Ali, Amina Senu, Norazak Wahi, Nadihah Almakayeel, Naif Ahmadian, Ali This study aims to develop a new strategy for solving partial differential equations with fractional derivatives (FPDEs) using artificial neural networks (ANNs). Numerical solutions to FPDEs are obtained through the Hermite wavelet neural network (HWNN) model. The Caputo fractional derivative is consistently applied throughout the research to address fractional-order partial differential problems. To enhance computational efficiency and expand the input pattern, the hidden layer is removed. A neural network (NN) model featuring a feed-forward architecture and error-back propagation without supervision is employed to optimize network parameters and minimize errors. Numerical illustrations are presented to demonstrate the effectiveness of this approach in preserving computational efficiency while solving FPDEs. Elsevier 2024-06-01 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/116395/1/116395%20v2.pdf Ali, Amina and Senu, Norazak and Wahi, Nadihah and Almakayeel, Naif and Ahmadian, Ali (2024) An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks. Communications in Nonlinear Science and Numerical Simulation, 137. art. no. 108121. ISSN 1007-5704; eISSN: 1007-5704 https://linkinghub.elsevier.com/retrieve/pii/S100757042400306X 10.1016/j.cnsns.2024.108121 |
| spellingShingle | Ali, Amina Senu, Norazak Wahi, Nadihah Almakayeel, Naif Ahmadian, Ali An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title | An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title_full | An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title_fullStr | An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title_full_unstemmed | An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title_short | An adaptive algorithm for numerically solving fractional partial differential equations using Hermite wavelet artificial neural networks |
| title_sort | adaptive algorithm for numerically solving fractional partial differential equations using hermite wavelet artificial neural networks |
| url | http://psasir.upm.edu.my/id/eprint/116395/ http://psasir.upm.edu.my/id/eprint/116395/ http://psasir.upm.edu.my/id/eprint/116395/ http://psasir.upm.edu.my/id/eprint/116395/1/116395%20v2.pdf |