Let Γ() denotes the gamma function of a real number ∉ {0, −1, −2, … }. Then the difference matrix Δ of a fractional order is defined as (Δ) = ∑ (−1) () ! (). Using the difference operator Δ , we introduce paranormed difference sequence spaces (Δ , , Λ,) and (Δ , , Λ,) of fractional orders involving lacunary sequence, ; modulus function, and multiplier sequence, Λ = (). We investigate topological structures of these spaces and examine various inclusion relations.