Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules
This research introduces a novel and robust numerical approach, the stochastic improved Simpson Method, specifically developed to solve Itô and Stratonovich stochastic nonlinear system of differential equations with fractional order. By extending the classical Simpson’s one-third rule with the expli...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Nonlinear Engineering |
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| Online Access: | https://doi.org/10.1515/nleng-2024-0070 |
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| _version_ | 1850067097277693952 |
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| author | Fareed Aisha F. Semary Mourad S. |
| author_facet | Fareed Aisha F. Semary Mourad S. |
| author_sort | Fareed Aisha F. |
| collection | DOAJ |
| description | This research introduces a novel and robust numerical approach, the stochastic improved Simpson Method, specifically developed to solve Itô and Stratonovich stochastic nonlinear system of differential equations with fractional order. By extending the classical Simpson’s one-third rule with the explicit product integration rectangle rule, the proposed method efficiently handles fractional derivatives of orders between 0 and 1, based on the Caputo derivative. The novelty of this approach lies in its enhanced accuracy and stability in addressing the unique challenges posed by both Itô and Stratonovich systems, outperforming traditional numerical techniques. Rigorous order analysis, conducted with Mathematica 12 software, demonstrates the robustness and precision of the method. Its effectiveness is further validated through four distinct numerical case studies, highlighting its superior performance in solving stochastic nonlinear system of differential equations with fractional order. |
| format | Article |
| id | doaj-art-d2bf940fc5ca46ee8404322923e5d55a |
| institution | DOAJ |
| issn | 2192-8029 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Nonlinear Engineering |
| spelling | doaj-art-d2bf940fc5ca46ee8404322923e5d55a2025-08-20T02:48:30ZengDe GruyterNonlinear Engineering2192-80292025-02-01141p. 12210.1515/nleng-2024-0070Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rulesFareed Aisha F.0Semary Mourad S.1Department of Electrical Engineering, College of Engineering, Prince Sattam bin Abdulaziz University, Al Kharj, 11942, Saudi ArabiaDepartment of Basic Engineering Sciences, Benha Faculty of Engineering, Benha University, Benha, EgyptThis research introduces a novel and robust numerical approach, the stochastic improved Simpson Method, specifically developed to solve Itô and Stratonovich stochastic nonlinear system of differential equations with fractional order. By extending the classical Simpson’s one-third rule with the explicit product integration rectangle rule, the proposed method efficiently handles fractional derivatives of orders between 0 and 1, based on the Caputo derivative. The novelty of this approach lies in its enhanced accuracy and stability in addressing the unique challenges posed by both Itô and Stratonovich systems, outperforming traditional numerical techniques. Rigorous order analysis, conducted with Mathematica 12 software, demonstrates the robustness and precision of the method. Its effectiveness is further validated through four distinct numerical case studies, highlighting its superior performance in solving stochastic nonlinear system of differential equations with fractional order.https://doi.org/10.1515/nleng-2024-0070stochastic differential equationswhite noisefractional-order systemssimpson’s rulecaputo derivative |
| spellingShingle | Fareed Aisha F. Semary Mourad S. Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules Nonlinear Engineering stochastic differential equations white noise fractional-order systems simpson’s rule caputo derivative |
| title | Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules |
| title_full | Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules |
| title_fullStr | Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules |
| title_full_unstemmed | Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules |
| title_short | Stochastic improved Simpson for solving nonlinear fractional-order systems using product integration rules |
| title_sort | stochastic improved simpson for solving nonlinear fractional order systems using product integration rules |
| topic | stochastic differential equations white noise fractional-order systems simpson’s rule caputo derivative |
| url | https://doi.org/10.1515/nleng-2024-0070 |
| work_keys_str_mv | AT fareedaishaf stochasticimprovedsimpsonforsolvingnonlinearfractionalordersystemsusingproductintegrationrules AT semarymourads stochasticimprovedsimpsonforsolvingnonlinearfractionalordersystemsusingproductintegrationrules |