We introduced certain new subclasses of analytic functions of complex order defined by fractional integrals involving Fox's H-functions in the unit disc and investigate the various properties and characteristics of analytic functions belonging to the subclasses Sn(λ,b,γ). We also defined an another subclass Rn(λ,b,γ) involving Fox's H- functions. Apart from deriving a set of coefficient bounds for each of these function classes, we establish several inclusion relationships involving the (n, δ) - neighbourhoods of analytic functions with negative coefficients belonging to these subclasses.