Research Article

Partial Soft Derivative

Volume: 7 Number: 1 March 4, 2024
EN

Partial Soft Derivative

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.

Keywords

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

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. [1] D. A. Molodtsov, Soft set theory – First results, Comput. Math. Appl., 37(4-5) (1999), 19–31.
  2. [2] D. A. Molodtsov, Soft Set Theory, URSS, 2004. (In Russian)
  3. [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. [4] D. A. Molodtsov, Higher order derivatives in soft analysis, Nechetkie Sistemy i Myagkie Vychisleniya, 14(1) (2019), 34–55. (In Russian)
  5. [5] D. A. Molodtsov, Principles of rational analysis – Continuity of functions, Nechetkie Sistemy i Myagkie Vychisleniya, 14(2) (2019), 126–141. (In Russian)
  6. [6] D. A. Molodtsov, Principles of rational analysis – Derivatives and integrals, Nechetkie Sistemy i Myagkie Vychisleniya, 15(1) (2020), 5–25. (In Russian)
  7. [7] S. Acharjee, D. A. Molodtsov, Soft rational line integral, Vestnik Udmurtskogo Universiteta, Matematika, Mekhanika, Komp’yuternye Nauki, 31(4) (2021), 578–596.
APA
Arslan, B., & Enginoğlu, S. (2024). Partial Soft Derivative. Communications in Advanced Mathematical Sciences, 7(1), 14-26. https://doi.org/10.33434/cams.1395130
AMA
1.Arslan B, Enginoğlu S. Partial Soft Derivative. Communications in Advanced Mathematical Sciences. 2024;7(1):14-26. doi:10.33434/cams.1395130
Chicago
Arslan, Burak, and Serdar Enginoğlu. 2024. “Partial Soft Derivative”. Communications in Advanced Mathematical Sciences 7 (1): 14-26. https://doi.org/10.33434/cams.1395130.
EndNote
Arslan B, Enginoğlu S (March 1, 2024) Partial Soft Derivative. Communications in Advanced Mathematical Sciences 7 1 14–26.
IEEE
[1]B. Arslan and S. Enginoğlu, “Partial Soft Derivative”, Communications in Advanced Mathematical Sciences, vol. 7, no. 1, pp. 14–26, Mar. 2024, doi: 10.33434/cams.1395130.
ISNAD
Arslan, Burak - Enginoğlu, Serdar. “Partial Soft Derivative”. Communications in Advanced Mathematical Sciences 7/1 (March 1, 2024): 14-26. https://doi.org/10.33434/cams.1395130.
JAMA
1.Arslan B, Enginoğlu S. Partial Soft Derivative. Communications in Advanced Mathematical Sciences. 2024;7:14–26.
MLA
Arslan, Burak, and Serdar Enginoğlu. “Partial Soft Derivative”. Communications in Advanced Mathematical Sciences, vol. 7, no. 1, Mar. 2024, pp. 14-26, doi:10.33434/cams.1395130.
Vancouver
1.Burak Arslan, Serdar Enginoğlu. Partial Soft Derivative. Communications in Advanced Mathematical Sciences. 2024 Mar. 1;7(1):14-26. doi:10.33434/cams.1395130