Fractional neural network approximation

• Published in: Computers & mathematics with applications (1987) Vol. 64; no. 6; pp. 1655 - 1676
• Main Author: Anastassiou, George A.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2012
• Subjects: Approximation; Fractional derivative; Modulus of continuity; Neural network fractional approximation; Quasi-interpolation operator; Sigmoidal and hyperbolic tangent functions; Sigmoidal and hyperbolic tangent functions; Neural network fractional approximation; Modulus of continuity; Quasi-interpolation operator; Fractional derivative
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2012.01.019

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.