International Journal of Nonlinear Analysis and Applications

Weighted approximation using neural network in terms of fractional modulus of smoothness of fractional derivative

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Sciences, AL-Mustansiriyah University, Baghdad, Iraq

2 Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq

Abstract

We introduce direct theorems for universal weighted approximation. This approximation in terms of weighted Ditzain-Totik modulus of smoothness for the fractional derivative of functions in Lp  (quasi-normed spaces).

Keywords

[1] G.A. Anastassiou, Univariate sigmoidal neural network approximation, J. Comput. Anal. Appl. 14(1) (2012).
[2] G.A. Anastassiou, Quantitative Approximations, Chapman & Hall, CRC, Boca Raton, New York, 2000.
[3] G.A. Anastassiou, Fractional representation formulae and right fractional inequalities, Math. Comput. Modell. 54(11-12) (2011) 3098–3115.
[4] G.A. Anastassiou, Inteligent Systems: Approximation by Artificial Neural Networks, Intelligent Systems Reference Library, vol. 19, Springer, Heidelberg, 2011.
[5] G.A. Anastassiou, Multivariate hyperbolic tangent neural network approximation, Comput. Math. 61 (2011) 809–821.
[6] K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, 2010.
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 3381-3394
  • Receive Date: 19 June 2021
  • Revise Date: 17 July 2021
  • Accept Date: 14 October 2021