Bewaard in:
| Hoofdauteurs: | , |
|---|---|
| Formaat: | Recurso digital |
| Taal: | Engels |
| Gepubliceerd in: |
Zenodo
2025
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| Onderwerpen: | |
| Online toegang: | https://doi.org/10.5281/zenodo.15079589 |
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Inhoudsopgave:
- <p>This paper presents a comprehensive extension of the Vonoroviskaya-Damasclin theorem, integrating fractional calculus into neural network operators to refine convergence analysis and improve approximation accuracy. By employing advanced fractional calculus techniques, we establish precise error bounds and significantly enhanced convergence rates, contributing to the theoretical development of neural network approximation in complex mathematical contexts. Our approach provides a rigorous framework for solving differential equations, particularly in fluid dynamics, where non-local and memory effects are essential. The incorporation of fractional differentiation into neural network operators demonstrates superior performance compared to traditional approximation methods, ensuring greater accuracy and adaptability. Supported by rigorous mathematical proofs, our findings introduce an adaptive framework that dynamically adjusts to local function smoothness, optimizing convergence rates and stability. Beyond its theoretical impact, this work lays the groundwork for future studies in stochastic models, high-dimensional approximations, and advanced numerical methods. The proposed methodology establishes a solid foundation for further advancements in neural network-based fractional approximations, highlighting the critical role of fractional calculus in refining modern approximation theories and computational techniques.</p>