Abstract
Here we consider the approximation of functions by sublinear positive operators with applications to a big variety of Max-Product operators under Caputo fractional differentiability. Our study is based on our general fractional results about positive sublinear operators. We produce Jackson type inequalities under simple initial conditions. So our approach is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of fractional derivative of the function under approximation. It follows Anastassiou, Caputo fractional approximation by sublinear operators (2017, submitted) [4].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Anastassiou, On right fractional calculus. Chaos, Solitons Fractals 42, 365–376 (2009)
G. Anastassiou, Fractional Korovkin theory. Chaos, Solitons Fractals 42, 2080–2094 (2009)
G. Anastassiou, Approximation by Sublinear Operators (2017, submitted)
G. Anastassiou, Caputo Fractional Approximation by Sublinear Operators (2017, submitted)
G. Anastassiou, L. Coroianu, S. Gal, Approximation by a nonlinear Cardaliaguet-Euvrard neural network operator of max-product kind. J. Comput. Anal. Appl. 12(2), 396–406 (2010)
B. Bede, L. Coroianu, S. Gal, Approximation by Max-Product Type Operators (Springer, Heidelberg, 2016)
R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)
K. Diethelm, The Analysis of Fractional Differential Equations (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)
L. Fejér, Über Interpolation, Göttingen Nachrichten, (1916), pp. 66–91
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)
G.G. Lorentz, Bernstein Polynomials, 2nd edn. (Chelsea Publishing Company, New York, 1986)
T. Popoviciu, Sur l’approximation de fonctions convexes d’order superieur. Mathematica (Cluj) 10, 49–54 (1935)
S.G. Samko, A.A. Kilbas and O.I. Marichev, Fractional Integrals and Derivatives, Theory and Applications, (Gordon and Breach, Amsterdam, 1993) [English translation from the Russian, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987)]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Anastassiou, G.A. (2018). Caputo Fractional Approximation Using Positive Sublinear Operators. In: Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators. Studies in Systems, Decision and Control, vol 147. Springer, Cham. https://doi.org/10.1007/978-3-319-89509-3_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-89509-3_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89508-6
Online ISBN: 978-3-319-89509-3
eBook Packages: EngineeringEngineering (R0)