Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators
This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy an...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Computation |
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| Online Access: | https://www.mdpi.com/2079-3197/12/1/14 |
| _version_ | 1827372518176980992 |
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| author | Nayereh Tanha Behrouz Parsa Moghaddam Mousa Ilie |
| author_facet | Nayereh Tanha Behrouz Parsa Moghaddam Mousa Ilie |
| author_sort | Nayereh Tanha |
| collection | DOAJ |
| description | This study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm’s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature. |
| first_indexed | 2024-03-08T11:00:51Z |
| format | Article |
| id | doaj.art-23fb760c7ecc4adab527fd3ee2dfbb52 |
| institution | Directory Open Access Journal |
| issn | 2079-3197 |
| language | English |
| last_indexed | 2024-03-08T11:00:51Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Computation |
| spelling | doaj.art-23fb760c7ecc4adab527fd3ee2dfbb522024-01-26T15:52:03ZengMDPI AGComputation2079-31972024-01-011211410.3390/computation12010014Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order OperatorsNayereh Tanha0Behrouz Parsa Moghaddam1Mousa Ilie2Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, IranDepartment of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, IranDepartment of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. Box 3516-41335, IranThis study presents an algorithmically efficient approach to address the complexities associated with nonlocal variable-order operators characterized by diverse definitions. The proposed method employs integro spline quasi interpolation to approximate these operators, aiming for enhanced accuracy and computational efficiency. We conduct a thorough comparison of the outcomes obtained through this approach with other established techniques, including finite difference, IQS, and B-spline methods, documented in the applied mathematics literature for handling nonlocal variable-order derivatives and integrals. The numerical results, showcased in this paper, serve as a compelling validation of the notable advantages offered by our innovative approach. Furthermore, this study delves into the impact of selecting different variable-order values, contributing to a deeper understanding of the algorithm’s behavior across a spectrum of scenarios. In summary, this research seeks to provide a practical and effective solution to the challenges associated with nonlocal variable-order operators, contributing to the applied mathematics literature.https://www.mdpi.com/2079-3197/12/1/14fractional calculusintegro splinequasi interpolationvariable-order fractional derivatives and integralsnumerical computation using splines |
| spellingShingle | Nayereh Tanha Behrouz Parsa Moghaddam Mousa Ilie Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators Computation fractional calculus integro spline quasi interpolation variable-order fractional derivatives and integrals numerical computation using splines |
| title | Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators |
| title_full | Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators |
| title_fullStr | Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators |
| title_full_unstemmed | Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators |
| title_short | Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators |
| title_sort | cutting edge computational approaches for approximating nonlocal variable order operators |
| topic | fractional calculus integro spline quasi interpolation variable-order fractional derivatives and integrals numerical computation using splines |
| url | https://www.mdpi.com/2079-3197/12/1/14 |
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