Fluorescence recovery after photobleaching (FRAP) is a common technique to probe mobility of fluorescently labeled proteins in biological membranes by monitoring the time-dependence of the spatially integrated fluorescence signals after a bleaching pulse. Discrimination by FRAP between free diffusion with an immobile fraction (FDIM) and the phenomenological model for anomalous diffusion based on the time-dependent diffusion coefficient (TDDC) is a challenging problem, requiring extremely long observation times for differentiation. Recently, rectangular FRAP (rFRAP) has been introduced for normal diffusion by considering not only the temporal but also spatial information, taking the effective point spread function of the optical system into account. In this work we provide an extension of rFRAP toward anomalous diffusion according to the continuous time random walk (CTRW). We explore whether the spatial information in rFRAP allows for enhanced discrimination between FDIM, TDDC, and CTRW in a single experiment within a feasible time window. Simulations indicate that rFRAP can indeed differentiate the different models by evaluating the spatial autocorrelation of the differences between the measured and fitted pixel values. Hence, rFRAP offers a tool that is capable of discriminating different types of diffusion at shorter time scales than in the case where spatial information is discarded.