In this paper, we extend the recently introduced concept of fractional wavelet transform to obtain directional subbands of an image. Fractional wavelet decomposition is based on two-channel unbalanced lifting structures whereby it is possible to decompose a given discrete-time signal x[n] sampled with period T into two sub-signals x 1[n] and x 2[n] whose average sampling periods are pT and qT, respectively. Fractions p and q are rational numbers satisfying the condition: 1/p+1/q=1. Filters used in the lifting structure are designed using the Lagrange interpolation formula. 2-d separable and non-separable extensions of the proposed fractional wavelet transform are developed. Using a non-separable unbalanced lifting structure, directional subimages for five different directions are obtained. © 2012 Springer-Verlag.