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We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have Formula: see text dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning Formula: see text-local derivations of such algebras is investigated and an example of solvable Leibniz algebra is given such that any Formula: see text-local derivation on it is a derivation, but which admits local derivations which are not derivations.
Ayupov et al. (Mon,) studied this question.
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