A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach
In this paper, a new Caputo discrete fractional model is introduced to capture the dynamics of English language learning. This model creates a strong foundation for examining language acquisition behaviors by including the learning process within the system. The proposed work not only presents an in...
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Elsevier
2025-06-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016125002213 |
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| author | Maria Aqsa Zafar Abbasi Muhammad Asif Zahoor Raja Kottakkaran Sooppy Nisar Muhammad Shoaib |
| author_facet | Maria Aqsa Zafar Abbasi Muhammad Asif Zahoor Raja Kottakkaran Sooppy Nisar Muhammad Shoaib |
| author_sort | Maria |
| collection | DOAJ |
| description | In this paper, a new Caputo discrete fractional model is introduced to capture the dynamics of English language learning. This model creates a strong foundation for examining language acquisition behaviors by including the learning process within the system. The proposed work not only presents an innovative discrete fractional model but also leverages machine learning techniques to estimate and analyze the learning process over time.To achieve numerical accuracy and stability, we employ Bayesian Regularization Artificial Neural Networks (BRA-NNs) as a machine learning-based computational solver. This approach ensures robust numerical simulations and enhances the predictive power of the model. Furthermore, the reliability of the proposed method is demonstrated through six fractional-order variants of the Fractional-Order English Language Mathematical Model (FOELMM), which are systematically derived and analyzed. The results are validated against the Fractional-Order Lotka-Volterra method, confirming the accuracy and robustness of the proposed machine learning-driven computational approach. • Development of a discrete Caputo fractional model for language learning. • Integration of machine learning techniques via Bayesian Regularization Artificial Neural Networks (BRA-NNs) for numerical simulations. • Validation of the model through the Fractional-Order Lotka-Volterra approach to ensure accuracy. |
| format | Article |
| id | doaj-art-9ddd63d053984e40a16f59fa67ccbe7c |
| institution | Matheson Library |
| issn | 2215-0161 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj-art-9ddd63d053984e40a16f59fa67ccbe7c2025-06-27T05:51:38ZengElsevierMethodsX2215-01612025-06-0114103375A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach Maria0Aqsa Zafar Abbasi1Muhammad Asif Zahoor Raja2Kottakkaran Sooppy Nisar3Muhammad Shoaib4Department of Foreign Languages and Applied Linguistics, Yuan Ze University, 135 Yuan-Tung Road, Chung Li 32003, TaiwanDepartment of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, PakistanFuture Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 0.3, Douliou, Yunlin 64002, TaiwanDepartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia; Corresponding authors.Yuan Ze University, AI Centre, Taoyuan 320, TaiwanIn this paper, a new Caputo discrete fractional model is introduced to capture the dynamics of English language learning. This model creates a strong foundation for examining language acquisition behaviors by including the learning process within the system. The proposed work not only presents an innovative discrete fractional model but also leverages machine learning techniques to estimate and analyze the learning process over time.To achieve numerical accuracy and stability, we employ Bayesian Regularization Artificial Neural Networks (BRA-NNs) as a machine learning-based computational solver. This approach ensures robust numerical simulations and enhances the predictive power of the model. Furthermore, the reliability of the proposed method is demonstrated through six fractional-order variants of the Fractional-Order English Language Mathematical Model (FOELMM), which are systematically derived and analyzed. The results are validated against the Fractional-Order Lotka-Volterra method, confirming the accuracy and robustness of the proposed machine learning-driven computational approach. • Development of a discrete Caputo fractional model for language learning. • Integration of machine learning techniques via Bayesian Regularization Artificial Neural Networks (BRA-NNs) for numerical simulations. • Validation of the model through the Fractional-Order Lotka-Volterra approach to ensure accuracy.http://www.sciencedirect.com/science/article/pii/S2215016125002213Caputo Fractional Model for English Learning |
| spellingShingle | Maria Aqsa Zafar Abbasi Muhammad Asif Zahoor Raja Kottakkaran Sooppy Nisar Muhammad Shoaib A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach MethodsX Caputo Fractional Model for English Learning |
| title | A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach |
| title_full | A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach |
| title_fullStr | A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach |
| title_full_unstemmed | A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach |
| title_short | A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization approach |
| title_sort | novel caputo fractional model for english language learning analysis and simulation with bayesian regularization approach |
| topic | Caputo Fractional Model for English Learning |
| url | http://www.sciencedirect.com/science/article/pii/S2215016125002213 |
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