Recently Baliarsingh and Dutta [11], [12] introduced the fractional difference operator Δα, defined by Δα(xk) =    and defined new classes of generalized difference sequence spaces of fractional order X(Γ, Δα, u) where X = {????∞, c, c0} . More recently, Kadak [21] studied strongly Cesàro and statistical difference sequence space of fractional order involving lacunary sequences using the fractional difference operator  is is any fixed sequence of positive real or complex numbers. Following Baliarsingh and Dutta [11], [12] and Kadak [21], we introduce paranormed difference sequence spaces  of fractional order involving lacunary sequence, θ and modulus function, f. We investigate topological structures of these spaces and examine various inclusion relations.