In the present paper we establish an important result involving a fractional differential operator given by Misra [5] for the product of H-function, general polynomial set and two general class of polynomials.On account of the general nature of the functions and the polynomials occurring in our main results a large number of simple results follow as its special cases. For the sake of illustration, we present here two special cases involving product of general class of polynomials and the generalized Riemann Zeta function.