  In this paper, we introduce the cohomology theory of relative Rota-Baxter
operators on Leibniz triple systems. We use the cohomological approach to study
linear and formal deformations of relative Rota-Baxter operators. In
particular, formal deformations and extendibility of order $n$ deformations of
a relative Rota-Baxter operators are also characterized in terms of the
cohomology theory. We also consider the relationship between cohomology of
relative Rota-Baxter operators on Leibniz algebras and associated Leibniz
triple systems.
