  Recently, relative Rota-Baxter (Lie/associative) algebras are extensively
studied in the literature from cohomological points of view. In this paper, we
consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the
object of our study. We construct an $L_\infty$-algebra that characterizes rRB
Leibniz algebras as its Maurer-Cartan elements. Then we define representations
of an rRB Leibniz algebra and introduce cohomology with coefficients in a
representation. As applications of cohomology, we study deformations and
abelian extensions of rRB Leibniz algebras.
