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    Symmetrized Neural Network Operators in Fractional Calculus: Caputo Derivatives, Asymptotic Analysis, and the Voronovskaya–Santos–Sales Theorem by Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales, Gislan Silveira Santos

    Published 2025-06-01
    “…Numerical experiments demonstrate a relative error reduction of up to <b>92.5%</b> when compared to classical quasi-interpolation operators, with observed convergence rates reaching <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">O</mi><mfenced separators="" open="(" close=")"><msup><mi>n</mi><mrow><mo>−</mo><mn>1.5</mn></mrow></msup></mfenced></mrow></semantics></math></inline-formula> under Caputo derivatives, using parameters <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>λ</mi><mo>=</mo><mn>3.5</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><mn>1.8</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>100</mn></mrow></semantics></math></inline-formula>. …”
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