Fractional neural network approximation. (English) Zbl 1268.41007
Summary: We study the univariate fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation sigmoidal and hyperbolic tangent neural network operators. These approximations are derived by establishing Jackson type inequalities involving the moduli of continuity of the right and left Caputo fractional derivatives of the engaged function. The approximations are pointwise and with respect to the uniform norm. The related feed-forward neural networks are with one hidden layer. Our fractional approximation results into higher order converges better than the ordinary ones.
MSC:
| 41A17 | Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities) |
| 41A30 | Approximation by other special function classes |
| 26A33 | Fractional derivatives and integrals |
| 41A36 | Approximation by positive operators |
Keywords:
sigmoidal and hyperbolic tangent functions; neural network fractional approximation; quasi-interpolation operator; modulus of continuity; fractional derivativeReferences:
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