  In this article, we have introduced the concept of \textit{geodesic
$(\alpha,E)$-invex set} and by using this concept the notion of
\textit{geodesic $(\alpha,E)$-preinvex functions} and \textit{geodesic
$(\alpha,E)$-invex functions} are developed on a Riemannian manifold. Moreover,
several properties and results are deduced within aforesaid functions. An
example is also constructed to illustrate the definition of geodesic
$(\alpha,E)$-invex set. We have also established an important relation between
geodesic $(\alpha,E)$-preinvex function and geodesic $(\alpha,E)$-invex
function in a complete Riemannian manifold.
