Geodesic
Higher order derivatives in soft analysis
Nečetkie sistemy i mâgkie vyčisleniâ, Tome 14 (2019) no. 1, pp. 34-55.

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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. 
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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)