  In this paper we establish some (presumably new) interesting expressions for
the composition of some well known fractional integral operators $
I^{\mu}_{a+}, D^{\mu}_{a+} $,$ I^{\gamma , \mu}_{a+}$ and also derive an
integral operator $\mathcal{H}^{w;m,n;\alpha}_{a+;p,q;\beta}$ whose kernel
involve the Fox's $H-$ function. By suitably specializing the coefficients and
the parameters in these functions we can get a large number of (new and known)
interesting expressions for the composition formulae which occur rather
frequently in many problems of engineering and mathematical analysis but here
we can mention only those which follow as particular cases of the Srivastava et
al.\cite{ZT}.
