  We study a generalized nonlocal theory of gravity which, in specific limits,
can become either the curvature non-local or teleparallel non-local theory.
Using the Noether Symmetry Approach, we find that the coupling functions coming
from the non-local terms are constrained to be either exponential or linear in
form. It is well known that in some non-local theories, a certain kind of
exponential non-local couplings are needed in order to achieve a renormalizable
theory. In this paper, we explicitly show that this kind of coupling does not
need to by introduced by hand, instead, it appears naturally from the
symmetries of the Lagrangian in flat Friedmann-Robertson-Walker cosmology.
Finally, we find de-Sitter and power law cosmological solutions for different
nonlocal theories. The symmetries for the generalized non-local theory is also
found and some cosmological solutions are also achieved under the full theory.
