Abstract
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.
Supporting Institution
Çanakkale Onsekiz Mart University
Project Number
FDR-2022-4206
Thanks
This study was supported by the Office of Scientific Research Projects Coordination at Çanakkale Onsekiz Mart University, Grant number: FDR-2022-4206.
References
- [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.
Abstract
Project Number
FDR-2022-4206
References
- [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.
Details
| Primary Language | English |
|---|---|
| Subjects | Pure Mathematics (Other) |
| Journal Section | Articles |
| Authors | |
| Project Number | FDR-2022-4206 |
| Early Pub Date | February 9, 2024 |
| Publication Date | March 4, 2024 |
| Submission Date | November 23, 2023 |
| Acceptance Date | January 30, 2024 |
| Published in Issue | Year 2024 Volume: 7 Issue: 1 |
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