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In this paper we show that the method for describing solvable Lie algebraswith given nilradical by means of non-nilpotent outer derivations of thenilradical is also applicable to the case of Leibniz algebras. Using thismethod we extend the classification of solvable Lie algebras with naturallygraded filiform Lie algebra to the case of Leibniz algebras. Namely, theclassification of solvable Leibniz algebras whose nilradical is a naturallygraded filiform Leibniz algebra is obtained.

Classification of solvable Leibniz algebras with naturally graded filiform nilradical