Partial Soft Derivative

Yıl 2024, Cilt: 7 Sayı: 1, 14 - 26, 04.03.2024

Burak Arslan Serdar Enginoğlu

https://doi.org/10.33434/cams.1395130

Öz

The concept of soft derivative, introduced by Molodtsov in 1999, is one of the fundamental concepts in soft analysis. The handled paper defines partial soft derivative and studies some of its basic properties, such as the relation between partial soft derivative and boundedness, some basic partial soft derivative rules, e.g., sum rule, constant multiple rule, and difference rule, the relation between soft derivative and partial soft derivative, the relation between classical partial derivative and partial soft derivative, and the geometric interpretation of partial soft derivative. Moreover, it exemplifies the theoretical part of the study and provides figures for the geometric interpretation. Finally, this study discusses the need for further research.

Anahtar Kelimeler

Partial soft derivative, Soft analysis, Soft derivative, Soft sets

Destekleyen Kurum

Çanakkale Onsekiz Mart University

Proje Numarası

FDR-2022-4206

Teşekkür

This study was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: FDR-2022-4206.

Kaynakça

• [1] D. A. Molodtsov, Soft set theory – First results, Comput. Math. Appl., 37(4-5) (1999), 19–31.
• [2] D. A. Molodtsov, Soft Set Theory, URSS, 2004. (In Russian)
• [3] D. A. Molodtsov, A. A. Sokolov, D. V. Kovkov, Basic foundations of soft analysis, Nechetkie Sistemy i Myagkie Vychisleniya, 2(1) (2007), 5–28. (In Russian)
• [4] D. A. Molodtsov, Higher order derivatives in soft analysis, Nechetkie Sistemy i Myagkie Vychisleniya, 14(1) (2019), 34–55. (In Russian)
• [5] D. A. Molodtsov, Principles of rational analysis – Continuity of functions, Nechetkie Sistemy i Myagkie Vychisleniya, 14(2) (2019), 126–141. (In Russian)
• [6] D. A. Molodtsov, Principles of rational analysis – Derivatives and integrals, Nechetkie Sistemy i Myagkie Vychisleniya, 15(1) (2020), 5–25. (In Russian)
• [7] S. Acharjee, D. A. Molodtsov, Soft rational line integral, Vestnik Udmurtskogo Universiteta, Matematika, Mekhanika, Komp’yuternye Nauki, 31(4) (2021), 578–596.