Fractional neural network approximation
Abstract
Here, 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. © 2012 Elsevier Ltd. All rights reserved.
Publication Title
Computers and Mathematics with Applications
Recommended Citation
Anastassiou, G. (2012). Fractional neural network approximation. Computers and Mathematics with Applications, 64 (6), 1655-1676. https://doi.org/10.1016/j.camwa.2012.01.019
