Geodesic
Principles of rational analysis - derivatives and integrals
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 15 (2020) no. 1, pp. 5-25.

Voir la notice de l'article provenant de la source Math-Net.Ru

Building on the basics of rational analysis is ongoing. Two concepts of a soft derivative are proposed. An analogue of Fermat's theorem is proved. For both variants of the soft derivative, the inverse operations of soft integration are constructed. Existence theorems and analogues of the differentiability properties of the classical upper limit integral are proved.
Keywords: rational analysis, soft derivatives of rational function, soft integral of rational function. 
@article{FSSC_2020_15_1_a0,
     author = {D. A. Molodtsov},
     title = {Principles of rational analysis - derivatives and integrals},
     journal = {Ne\v{c}etkie sistemy i m\^agkie vy\v{c}isleni\^a},
     pages = {5--25},
     publisher = {mathdoc},
     volume = {15},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FSSC_2020_15_1_a0/}
}
TY  - JOUR
AU  - D. A. Molodtsov
TI  - Principles of rational analysis - derivatives and integrals
JO  - Nečetkie sistemy i mâgkie vyčisleniâ
PY  - 2020
SP  - 5
EP  - 25
VL  - 15
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FSSC_2020_15_1_a0/
LA  - ru
ID  - FSSC_2020_15_1_a0
ER  - 
%0 Journal Article
%A D. A. Molodtsov
%T Principles of rational analysis - derivatives and integrals
%J Nečetkie sistemy i mâgkie vyčisleniâ
%D 2020
%P 5-25
%V 15
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FSSC_2020_15_1_a0/
%G ru
%F FSSC_2020_15_1_a0
D. A. Molodtsov. Principles of rational analysis - derivatives and integrals. Nečetkie sistemy i mâgkie vyčisleniâ, Tome 15 (2020) no. 1, pp. 5-25. http://geodesic.mathdoc.fr/item/FSSC_2020_15_1_a0/

[1] Molodtsov D. A., “Principles of rational analysis - continuity of functions”, Fuzzy Systems and Soft Computing, 14:2 (2019), 126–141 (in Russian) | DOI

[2] Orlov I. V., Stonyakin F. S., New methods of non-smooth analysis and their applications in vector integration and optimization theory, Diajpi, Simferopol, 2016, 318 pp. (in Russian)

[3] Demyanov V. F., Shomesova V. K., “Conditional subdifferentials of convex functions”, Doklady Akademii Nauk SSSR, 242:4 (1978), 753–756 (in Russian) | MR | Zbl