Framelets generalize orthogonal wavelets by adding the desired properties of
redundancy in their systems and flexibility in their construction. These
extra features greatly improve their performance over orthogonal wavelets in
applications such as image denoising and data processing. The main objective
of this paper is to study fractional framelets associted with the fractional
refinable functions that are obtained via unitary extension principles.
Furthermore all the possible solutions of the matrix equations that arise in
the study are obtained. Towards the end it is shown that the problem of
extension has always a solution with two fractional framelets.