The difference operator of fractional order and its applications is studied by P. Baliarsingh in [8], introduced the new sequence spaces using difference operator of fractional order in [9] and examined some topological properties of these sequence spaces and also computed their dual spaces. In this paper, using the definition of difference operator of fractional order and using definitions which are given in [6] by M. Mursaleen and A. K. Noman, the authors introduced the sequence spaces c₀(Δ_λ^(α)) and c (Δ_λ^(α) ) which are BK-spaces of non-absolute type. The authors also proved that c₀(Δ_λ^(α)) and c(Δ_λ^(α)) spaces are linearly isomorphic to the classical sequence spaces c₀ and c, respectively. Lastly, we determine the Schauder basis of the c(Δ_λ^(α)),c₀(Δ_λ^(α)) and we compute the α-, β- and γ- duals of these spaces.