A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense
This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts th...
| Main Authors: | , , , , |
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| Format: | Article |
| Published: |
Springer
2022
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| Online Access: | http://psasir.upm.edu.my/id/eprint/100245/ |
| _version_ | 1848863273239183360 |
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| author | Shloof, A. M. Senu, N. Ahmadian, A. Pakdaman, M. Salahshour, S. |
| author_facet | Shloof, A. M. Senu, N. Ahmadian, A. Pakdaman, M. Salahshour, S. |
| author_sort | Shloof, A. M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach. |
| first_indexed | 2025-11-15T13:30:18Z |
| format | Article |
| id | upm-100245 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:30:18Z |
| publishDate | 2022 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1002452024-03-18T05:08:44Z http://psasir.upm.edu.my/id/eprint/100245/ A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense Shloof, A. M. Senu, N. Ahmadian, A. Pakdaman, M. Salahshour, S. This paper attempts to create an artificial neural networks (ANNs) technique for solving well-known fractal-fractional differential equations (FFDEs). FFDEs have the advantage of being able to help explain a variety of real-world physical problems. The technique implemented in this paper converts the original differential equation into a minimization problem using a suggested truncated power series of the solution function. Next, answer to the problem is obtained via computing the parameters with highly precise neural network model. We can get a good approximate solution of FFDEs by combining the initial conditions with the ANNs performance. Examples are provided to portray the efficiency and applicability of this method. Comparison with similar existing approaches are also conducted to demonstrate the accuracy of the proposed approach. Springer 2022-02-15 Article PeerReviewed Shloof, A. M. and Senu, N. and Ahmadian, A. and Pakdaman, M. and Salahshour, S. (2022) A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense. Engineering with Computers, 39. pp. 505-515. ISSN 0177-0667; ESSN: 1435-5663 https://link.springer.com/article/10.1007/s00366-022-01607-8 10.1007/s00366-022-01607-8 |
| spellingShingle | Shloof, A. M. Senu, N. Ahmadian, A. Pakdaman, M. Salahshour, S. A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title | A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title_full | A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title_fullStr | A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title_full_unstemmed | A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title_short | A new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized Caputo sense |
| title_sort | new iterative technique for solving fractal-fractional differential equations based on artificial neural network in the new generalized caputo sense |
| url | http://psasir.upm.edu.my/id/eprint/100245/ http://psasir.upm.edu.my/id/eprint/100245/ http://psasir.upm.edu.my/id/eprint/100245/ |