It has been widely concerned to apply fractional partial differential equations in image processing, especially in the image denoising and image Super Resolution (SR) reconstruction. The current research results have shown the advantages and effects of fractional order applications. The theory and model of fractional partial differential equations in image denoising and image super-resolution reconstruction were introduced and discussed. The simulation results show that the methods based on fractional partial differential equations has more advantages than the methods based on integer order partial differential equations in terms of denoising and reducing the staircase effect. Finally, the related research problems were pointed out.