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Synthetic aperture radar (SAR) systems are used to form high-resolution images from radar backscatter signals. The fractional Fourier transform (FrFT), which is a generalised form of the well-known Fourier transform, has opened up the possibility of a new range of potentially promising and useful applications that involve the use and detection of chirp signals that include pattern recognition and SAR imaging. In this study a time variant problem associated with the use of the FrFT for SAR processing is addressed and a new algorithm is presented that resolves this problem. Two new FrFT-based SAR processing algorithms are presented namely the FrRDA and the eFrCSA that are shown to improve the well-established range-Doppler and chirp-scaling algorithms for SAR processing. The performance of the algorithms are assessed using simulated and real Radarsat-1 data sets. The results confirm that the FrFT-based SAR processing methods provide enhanced resolution yielding both lower side lobes effects and improved target detection.