Local and 2-local 1 2-derivations on solvable Lie algebras with a filiform nilradical

This paper is devoted to the study of local and two-local [Formula: see text]-derivations of rank one or zero solvable Lie algebras with a filiform nilradical. Let [Formula: see text] be the [Formula: see text]-dimensional Witt algebra, let [Formula: see text] be the [Formula: see text]-dimensional special filiform algebra and let [Formula: see text], [Formula: see text] be the their maximal solvable extensions, respectively. We find a general form of the local [Formula: see text]-derivations on [Formula: see text] and [Formula: see text]. Also, we prove that solvable Lie algebras [Formula: see text] or [Formula: see text], admit local [Formula: see text]-derivations which are not [Formula: see text]-derivations. Moreover, similar results concerning two-local [Formula: see text]-derivations of such algebras are obtained for solvable Lie algebras mentioned above.