An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative
A new differential operators class has been discovered utilising fractional and variable-order fractal Atangana-Baleanu derivatives that have inspired the develop-ment of differential equations new class. Physical phenomena with variable memory and fractal variable dimension can be described using t...
| Main Authors: | , , , , |
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| Format: | Article |
| Published: |
Horizon Research Publishing Corporation
2023
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| Online Access: | http://psasir.upm.edu.my/id/eprint/106548/ |
| _version_ | 1848864781162774528 |
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| author | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. |
| author_facet | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. |
| author_sort | Basim, M. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A new differential operators class has been discovered utilising fractional and variable-order fractal Atangana-Baleanu derivatives that have inspired the develop-ment of differential equations new class. Physical phenomena with variable memory and fractal variable dimension can be described using these operators. In addition, the primary goal of this study is to use the operation matrix based on shifted Legendre polynomials to obtain numerical solutions with respect to this new differential equations class, which will aid us in solving the issue and transforming it into an algebraic equation system. This method is employed in solving two forms of fractal fractional differential equations: non-linear and linear. The suggested strategy is contrasted with the mixture of two-step Lagrange polynomials, the predictor-corrector algorithm, as well as the fractional calculus methods fundamental theorem, using numerical examples to demonstrate its accuracy and simplicity. The estimation error was proposed to contrast the results of the suggested methods and the exact solution to the problems. The proposed approach could apply to a wider class of biological systems, such as mathematical modelling of infectious disease dynamics and other important areas of study, such as economics, finance, and engineering. We are confident that this paper will open many new avenues of investigation for modelling real-world system problems. |
| first_indexed | 2025-11-15T13:54:16Z |
| format | Article |
| id | upm-106548 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-15T13:54:16Z |
| publishDate | 2023 |
| publisher | Horizon Research Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-1065482024-08-08T02:56:03Z http://psasir.upm.edu.my/id/eprint/106548/ An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. A new differential operators class has been discovered utilising fractional and variable-order fractal Atangana-Baleanu derivatives that have inspired the develop-ment of differential equations new class. Physical phenomena with variable memory and fractal variable dimension can be described using these operators. In addition, the primary goal of this study is to use the operation matrix based on shifted Legendre polynomials to obtain numerical solutions with respect to this new differential equations class, which will aid us in solving the issue and transforming it into an algebraic equation system. This method is employed in solving two forms of fractal fractional differential equations: non-linear and linear. The suggested strategy is contrasted with the mixture of two-step Lagrange polynomials, the predictor-corrector algorithm, as well as the fractional calculus methods fundamental theorem, using numerical examples to demonstrate its accuracy and simplicity. The estimation error was proposed to contrast the results of the suggested methods and the exact solution to the problems. The proposed approach could apply to a wider class of biological systems, such as mathematical modelling of infectious disease dynamics and other important areas of study, such as economics, finance, and engineering. We are confident that this paper will open many new avenues of investigation for modelling real-world system problems. Horizon Research Publishing Corporation 2023 Article PeerReviewed Basim, M. and Senu, N. and Ahmadian, A. and Ibrahim, Z. B. and Salahshour, S. (2023) An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative. Mathematics and Statistics, 11 (1). 149- 159. ISSN 2332-2071; ESSN: 2332-2144 https://www.hrpub.org/journals/article_info.php?aid=12889 10.13189/ms.2023.110117 |
| spellingShingle | Basim, M. Senu, N. Ahmadian, A. Ibrahim, Z. B. Salahshour, S. An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title | An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title_full | An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title_fullStr | An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title_full_unstemmed | An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title_short | An effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| title_sort | effective spectral approach to solving fractal differential equations of variable order based on the non-singular kernel derivative |
| url | http://psasir.upm.edu.my/id/eprint/106548/ http://psasir.upm.edu.my/id/eprint/106548/ http://psasir.upm.edu.my/id/eprint/106548/ |