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.