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 aM ≠ 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 α, then H (x1, …,xnR n D(H a n (M))) is a homomorphic image of D(M), where H b i (−) 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 (x1, …,xn)R n (D(H a n (M)))) ⋟ D(D(M)).