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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...

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Main Authors: Ali, Amina Hassan, Senu, Norazak, Ahmadian, Ali
Format: Article
Language:English
Published: Institute of Physics 2024
Online Access:http://psasir.upm.edu.my/id/eprint/114374/1/114374.pdf
http://psasir.upm.edu.my/id/eprint/114374/
https://iopscience.iop.org/article/10.1088/1402-4896/ad7c93
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spelling my.upm.eprints.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
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
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.
format Article
author Ali, Amina Hassan
Senu, Norazak
Ahmadian, Ali
spellingShingle Ali, Amina Hassan
Senu, Norazak
Ahmadian, Ali
Efficient solutions to time-fractional telegraph equations with Chebyshev neural networks
author_facet Ali, Amina Hassan
Senu, Norazak
Ahmadian, Ali
author_sort Ali, Amina Hassan
title 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_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_sort efficient solutions to time-fractional telegraph equations with chebyshev neural networks
publisher Institute of Physics
publishDate 2024
url http://psasir.upm.edu.my/id/eprint/114374/1/114374.pdf
http://psasir.upm.edu.my/id/eprint/114374/
https://iopscience.iop.org/article/10.1088/1402-4896/ad7c93
_version_ 1823093135351218176
score 13.244413

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