A novel caputo fractional model for english language learning: Analysis and simulation with bayesian regularization...

Area of Science:

• Applied Mathematics
• Computational Linguistics
• Machine Learning

Background:

• Language acquisition is a complex process that benefits from mathematical modeling.
• Fractional calculus offers advanced tools for modeling dynamic systems.
• Integrating computational methods can improve the analysis of learning behaviors.

Purpose of the Study:

• To introduce a new Caputo discrete fractional model for English language learning.
• To apply machine learning techniques for estimating and analyzing language acquisition dynamics.
• To validate the proposed model's accuracy and robustness.

Main Methods:

• Development of a discrete Caputo fractional model for language learning.
• Utilization of Bayesian Regularization Artificial Neural Networks (BRA-NNs) as a computational solver.
• Derivation and analysis of six fractional-order variants of the Fractional-Order English Language Mathematical Model (FOELMM).

Main Results:

• The proposed discrete fractional model effectively captures English language learning dynamics.
• BRA-NNs provided accurate and stable numerical simulations for the learning process.
• Validation against the Fractional-Order Lotka-Volterra method confirmed the model's reliability.

Conclusions:

• The integration of discrete fractional calculus and machine learning offers a powerful approach to studying language acquisition.
• The developed model and computational solver provide a robust framework for analyzing learning behaviors.
• This work lays the groundwork for further research in computational language learning models.