Abstract
This chapter deals with the determination of the fractional rate of convergence to the unit of some neural network operators, namely, the normalized bell and “squashing” type operators.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G.A. Anastassiou, Rate of convergence of some neural network operators to the unit-univariate case. J. Math. Anal. Appl. 212, 237–262 (1997)
G.A. Anastassiou, On right fractional calculus. Chaos, Solitons Fractals 42, 365–376 (2009)
G.A. Anastassiou, Fractional korovkin theory. Chaos, Solitons Fractals 42(4), 2080–2094 (2009)
G.A. Anastassiou, Fractional Differentiation Inequalities (Springer, New York, 2009)
G.A. Anastassiou, Quantitative approximation by fractional smooth picard singular operators. Math. Eng. Sci. Aerosp. 2(1), 71–87 (2011)
G.A. Anastassiou, Fractional representation formulae and right fractional inequalities. Math. Comput. Model. 54(11–12), 3098–3115 (2011)
G.A. Anastassiou, Fractional approximation by normalized bell and squashing type neural network operators. New Math. Nat. Comput. 9(1), 43–63 (2013)
P. Cardaliaguet, G. Euvrard, Approximation of a function and its derivative with a neural network. Neural Netw. 5, 207–220 (1992)
K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, vol. 2004 (Springer, Heidelberg, 2010)
A.M.A. El-Sayed, M. Gaber, On the finite Caputo and finite Riesz derivatives. Electron. J. Theor. Phys. 3(12), 81–95 (2006)
G.S. Frederico, D.F.M. Torres, Fractional optimal control in the sense of Caputo and the fractional Noether’s theorem. Int. Math. Forum 3(10), 479–493 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Anastassiou, G.A. (2016). Fractional Approximation by Normalized Bell and Squashing Type Neural Networks. In: Intelligent Systems II: Complete Approximation by Neural Network Operators. Studies in Computational Intelligence, vol 608. Springer, Cham. https://doi.org/10.1007/978-3-319-20505-2_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-20505-2_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-20504-5
Online ISBN: 978-3-319-20505-2
eBook Packages: EngineeringEngineering (R0)