Local derivations on solvable Lie algebras with a filiform nilradical

This paper is devoted to the study of local 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 their maximal solvable extensions, respectively. We find a general form of the local derivations on [Formula: see text] and [Formula: see text] In particular, we show that the spaces [Formula: see text] and [Formula: see text] equipped with Lie brackets are Lie algebras. Finally, we shall find a general form of rank zero solvable Lie algebra with a metabelian filiform nilradical.