Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 13 1 2022 03 01 Weighted approximation using neural network in terms of fractional modulus of smoothness of fractional derivative 3381 3394 6098 10.22075/ijnaa.2022.6098 EN Amenah Hassan Ibrahim Department of Mathematics, College of Sciences, AL-Mustansiriyah University, Baghdad, Iraq Eman Samir Bhaya Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq Eman Ali Hessen Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq Journal Article 2021 06 19 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 $L_p$  (quasi-normed spaces). https://ijnaa.semnan.ac.ir/article_6098_35660f966a0671b39822333fcc45cc38.pdf