%0 Journal Article %T Nearly $k-th$ Partial Ternary Cubic $*$-Derivations On Non-Archimedean $\ell$-Fuzzy $C^{*}$-Ternary Algebras %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A Abolfathi, Mohammad Ali %D 2022 %\ 09/01/2022 %V 19 %N 3 %P 13-33 %! Nearly $k-th$ Partial Ternary Cubic $*$-Derivations On Non-Archimedean $\ell$-Fuzzy $C^{*}$-Ternary Algebras %K Partial ternary derivation %K Cubic derivation %K Non-Archimedean $\ell$-fuzzy algebra %K $C^{*}$-ternary algebra %K Hyers-Ulam-Rasias stability %R 10.22130/scma.2021.543926.1026 %X In this paper, we investigate approximations of the $k-th$ partial ternary cubic derivations on non-Archimedean $\ell$-fuzzy Banach ternary algebras and non-Archimedean $\ell$-fuzzy $C^{*}$-ternary algebras. First, we study non-Archimedean and $\ell$-fuzzy spaces, and then  prove the stability of partial ternary cubic $*$-derivations on non-Archimedean $\ell$-fuzzy $C^{*}$-ternary algebras. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis. %U https://scma.maragheh.ac.ir/article_251968_1124b5bfb4a5fd95ef9179be88a44ba4.pdf