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Weighted approximation using neural network in terms of fractional modulus of smoothness of fractional derivative | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3381-3394 اصل مقاله (408.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6098 | ||
| نویسندگان | ||
| Amenah Hassan Ibrahim* 1؛ Eman Samir Bhaya2؛ Eman Ali Hessen2 | ||
| 1Department of Mathematics, College of Sciences, AL-Mustansiriyah University, Baghdad, Iraq | ||
| 2Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Babylon, Iraq | ||
| تاریخ دریافت: 29 خرداد 1400، تاریخ بازنگری: 26 تیر 1400، تاریخ پذیرش: 22 مهر 1400 | ||
| چکیده | ||
| 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). | ||
| کلیدواژهها | ||
| Ditzain-Totik modulus؛ quasi-norm؛ weighted approximation | ||
| مراجع | ||
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[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. | ||
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