Abstract
In this paper, we introduce Padovan difference sequence spaces of fractional-order alpha, l(p)((P) over tilde ((alpha))) (1 <= p <= infinity) by the composition of the fractional-order difference operator Delta((alpha)) and the Padovan matrix (P) over bar = ((p) over tilde (nk)) defined by Delta((alpha))(k)(x) = Sigma(infinity)(i=0)(-1)(i) Gamma(alpha+1)/i vertical bar Gamma(alpha- i+1)x(k-i) and
(P) over tilde (nk) = {(P) over tilde (k)/(P) over tilde (n+5) - 2 (0 <= k <= n), 0 (k > n),
respectively, where the sequence ((p) over tilde (k)) is the Padovan sequence. We give some topological properties, Schauder basis and alpha-, beta- and gamma-duals of the newly defined spaces. We characterize certain matrix classes related to the l(p)((P) over tilde ((alpha))) space. Finally, we characterize certain classes of compact operators on l(p)((P) over tilde ((alpha))) using Hausdorff measure of noncompactness.