%0 Journal Article
%T Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Ibrahim, Amenah Hassan
%A Bhaya, Eman Samir
%A Hessen, Eman Ali
%D 2022
%\ 03/01/2022
%V 13
%N 1
%P 3305-3317
%! Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network
%K Approximation
%K Ditzain-Totik modulus
%K higher-order fractal approximation
%K partial Caputo models
%K partial neural network
%K Sobolev space
%R 10.22075/ijnaa.2022.6083
%X Some scientists studied the weighted approximation of the partial neural network, but in this paper, we studied the weighted Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ of the partial neural network and this approximation of the real-valued functions over a compressed period by the tangent sigmoid and quasi-interpolation operators. These approximations measurable left and right partial Caputo models of the committed function. Approximations are bitmap with respect to the standard base. Feed-forward neural networks with a single hidden layer. Our higher-order fractal approximation results in better convergence than normal approximation with some applications. All proved results are in $L_p[X]$ spaces, where $0{<}p{<}1$
%U https://ijnaa.semnan.ac.ir/article_6083_1d98171dceb1462d76cb7ec50214c228.pdf