Let (R,m) be a commutative Noetherian local ring with non-zero identity, a a proper ideal of R and M a finitely generated R-module with a M\\neq M. Let D(-):=Hom_R(-,E) be the Matlis dual functor, where E:=E(R/m) is the injective hull of the residue field R/m. In this paper, by using a complex which involves modules of generalized fractions, we show that, if x_1, ... ,x_n is a regular sequence on M contained in a, then H^n_(x_1, ... ,x_n)R (D(H^n_a(M))) is a homomorphic image of D(M), where H^i_b(-) is the i-th local cohomology functor with respect to an ideal b of R. By applying this result, we study some conditions on a certain module of generalized fractions under which D(H^n_(x_1,... ,x_n)(D(H^n_a(M))))\\cong D(D(M)).

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