Let $mathcal{A}$ be a Banach ternary algebra over a scalar field R or C and $mathcal{X}$ be a ternary Banach $mathcal{A}$-module. A quartic mapping $D;:;(mathcal{A},[;]_{mathcal{A}}){ ightarrow}(mathcal{X},[;]_{mathcal{X}})$ is called a $4^{th}$- order ternary derivation if $D([x,y,z])=[D(x),y^4,z^4]+[x^4,D(y),z^4]+[x^4,y^4,D(z)]$ for all $x,y,z{in}mathcal{A}$. In this paper, we prove Ulam stability generalizations of $4^{th}$- order ternary derivations associated to the following JMRassias quartic functional equation on fr$acute{e}$che algebras: $$f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$$.