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Ibrahim, Amenah, Bhaya, Eman Samir, Hessen, Eman Ali. (1400). Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network. هنرهای کاربردی, 13(1), 3305-3317. doi: 10.22075/ijnaa.2022.6083
Amenah Hassan Ibrahim; Eman Samir Bhaya; Eman Ali Hessen. "Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network". هنرهای کاربردی, 13, 1, 1400, 3305-3317. doi: 10.22075/ijnaa.2022.6083
Ibrahim, Amenah, Bhaya, Eman Samir, Hessen, Eman Ali. (1400). 'Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network', هنرهای کاربردی, 13(1), pp. 3305-3317. doi: 10.22075/ijnaa.2022.6083
Ibrahim, Amenah, Bhaya, Eman Samir, Hessen, Eman Ali. Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network. هنرهای کاربردی, 1400; 13(1): 3305-3317. doi: 10.22075/ijnaa.2022.6083

Ditzain-Totik modulus of smoothness for the fractional derivative of functions in $L_p$ space of the partial neural network

International Journal of Nonlinear Analysis and Applications
دوره 13، شماره 1، خرداد 2022، صفحه 3305-3317    اصل مقاله (419.61 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6083
نویسندگان
Amenah Hassan Ibrahim* 1؛ Eman Samir Bhaya2؛ Eman Ali Hessen1
1Department of Mathematics, Collage of Sciences, AL-Mustansiriyah University, Baghdad, Iraq
2Department of Mathematics, Collage of Education for Pure Sciences, University of Babylon, Iraq
تاریخ دریافت: 21 خرداد 1400،  تاریخ بازنگری: 17 شهریور 1400،  تاریخ پذیرش: 27 مهر 1400 
چکیده
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 $0{<}p{<}1$
کلیدواژه‌ها
approximation؛ Ditzain-Totik modulus؛ higher-order fractal approximation؛ partial Caputo models؛ partial neural network؛ Sobolev space
مراجع

[1] G.A. Anastassiou, Univariate sigmoidal neural network approximation, J. Comput. Anal. Appl. 14(10 (2012).

[2] G.A. Anastassiou, Quantitative Approximations, Chapman&Hall, CRC, Boca Raton, New York, 2001.

[3] G.A. Anastassiou, Fractional representation formulae and right fractional inequalities, Math. Comput. Model. 54 (11–12)(2011) 3098–3115.

[4] G.A. Anastassiou, Intelligent 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.

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