In many real applications, traditional super-resolution (SR) methods fail to provide high-resolution images due to objectionable blur and inaccurate registration of input low-resolution images. Only integer resolution enhancement factors, such as 2 or 3, are often considered, but non-integer factors between 1 and 2 are also important in real cases. We introduce a method to SR and deconvolution, which assumes no prior information about the shape of degradation blurs, incorporates registration parameters, and is properly defined for any rational (fractional) resolution factor. The method minimizes a regularized energy function with respect to the high-resolution image and blurs, where regularization is carried out in both the image and blur domains. The blur regularization is based on a generalized multi-channel blind deconvolution constraint derived in the paper. An extension to color images is briefly discussed. Experiments on real data illustrate robustness to noise and other advantages of the method.