Geodesic
Higher order derivatives in soft analysis
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 1, pp. 34-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper proposes new approaches to the definition of soft derivatives of higher orders, based not on the reapplication of a soft derivative of the first order, but on the Taylor approximation formula. Two variants of such soft derivatives were implemented, their properties were studied and inverse operations (soft integrals) were constructed and the properties of these operations were established.
Keywords: soft derivatives, soft almost continuity, soft integrals, almost integrals. 
@article{FSSC_2019_14_1_a2,
     author = {D. A. Molodtsov},
     title = {Higher order derivatives in soft analysis},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {34--55},
     year = {2019},
     volume = {14},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2019_14_1_a2/}
}
TY  - JOUR
AU  - D. A. Molodtsov
TI  - Higher order derivatives in soft analysis
JO  - Nečetkie sistemy i mâgkie vyčisleniâ
PY  - 2019
SP  - 34
EP  - 55
VL  - 14
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/FSSC_2019_14_1_a2/
LA  - ru
ID  - FSSC_2019_14_1_a2
ER  - 
%0 Journal Article
%A D. A. Molodtsov
%T Higher order derivatives in soft analysis
%J Nečetkie sistemy i mâgkie vyčisleniâ
%D 2019
%P 34-55
%V 14
%N 1
%U http://geodesic.mathdoc.fr/item/FSSC_2019_14_1_a2/
%G ru
%F FSSC_2019_14_1_a2
D. A. Molodtsov. Higher order derivatives in soft analysis. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 1, pp. 34-55. http://geodesic.mathdoc.fr/item/FSSC_2019_14_1_a2/

[1] Molodtsov D. A., Stability of the principles of optimality, Nauka Publ., Moscow, 1987 (in Russian) | MR

[2] Molodtsov D. A., Priblizhennyj integral v mnogomernom sluchae, Vychislitelnyj Tsentr Akademii nauk SSSR, M., 1989 (in Russian)

[3] Molodtsov D. A., K obshchej teorii abstraktnogo intervalnogo integrala, Vychislitelnyj Tsentr Akademii nauk SSSR, M., 1991 (in Russian)

[4] Molodtsov D. A., “Soft differential equation”, Computational Mathematics and Mathematical Physics, 40:8 (2000), 1116–1128 | MR | Zbl

[5] Molodtsov D. A., “Myagkie topologicheskie konstruktsii”, Fuzzy Systems and Soft Computing, 10:2 (2015), 115–153 (in Russian) | MR | Zbl

[6] Molodtsov D. A., Soft set theory, URSS Publ., M., 2004 (in Russian)