Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method
In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compar...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/3218213 |
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| _version_ | 1832564923530477568 |
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| author | Saadia Masood Muhammad Naeem Roman Ullah Saima Mustafa Abdul Bariq |
| author_facet | Saadia Masood Muhammad Naeem Roman Ullah Saima Mustafa Abdul Bariq |
| author_sort | Saadia Masood |
| collection | DOAJ |
| description | In this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet-based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations. |
| format | Article |
| id | doaj-art-ec3bdd0c41a0439c99307c9780d9c44b |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ec3bdd0c41a0439c99307c9780d9c44b2025-02-03T01:10:00ZengWileyComplexity1099-05262022-01-01202210.1155/2022/3218213Analysis of the Fractional-Order Delay Differential Equations by the Numerical MethodSaadia Masood0Muhammad Naeem1Roman Ullah2Saima Mustafa3Abdul Bariq4Department of Mathematics and StatisticsDeanship of Joint First Year Umm Al-Qura University MakkahDepartment of General RequirementsDepartment of Mathematics and StatisticsDepartment of MathematicsIn this study, we implemented a new numerical method known as the Chebyshev Pseudospectral method for solving nonlinear delay differential equations having fractional order. The fractional derivative is defined in Caputo manner. The proposed method is simple, effective, and straightforward as compared to other numerical techniques. To check the validity and accuracy of the proposed method, some illustrative examples are solved by using the present scenario. The obtained results have confirmed the greater accuracy than the modified Laguerre wavelet method, the Chebyshev wavelet method, and the modified wavelet-based algorithm. Moreover, based on the novelty and scientific importance, the present method can be extended to solve other nonlinear fractional-order delay differential equations.http://dx.doi.org/10.1155/2022/3218213 |
| spellingShingle | Saadia Masood Muhammad Naeem Roman Ullah Saima Mustafa Abdul Bariq Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method Complexity |
| title | Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method |
| title_full | Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method |
| title_fullStr | Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method |
| title_full_unstemmed | Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method |
| title_short | Analysis of the Fractional-Order Delay Differential Equations by the Numerical Method |
| title_sort | analysis of the fractional order delay differential equations by the numerical method |
| url | http://dx.doi.org/10.1155/2022/3218213 |
| work_keys_str_mv | AT saadiamasood analysisofthefractionalorderdelaydifferentialequationsbythenumericalmethod AT muhammadnaeem analysisofthefractionalorderdelaydifferentialequationsbythenumericalmethod AT romanullah analysisofthefractionalorderdelaydifferentialequationsbythenumericalmethod AT saimamustafa analysisofthefractionalorderdelaydifferentialequationsbythenumericalmethod AT abdulbariq analysisofthefractionalorderdelaydifferentialequationsbythenumericalmethod |