Breast cancer is considered one of the most common cancers among women worldwide. It is one of the leading causes of mortality and disability in women. Early diagnosis of this disease may increase the chance of recovery and reduce mortality. The primary goal of mammography is the early diagnosis of breast cancer. Breast cancer in its early stages may be asymptomatic, but it can be diagnosed by mammography. Several methods are used for diagnosing breast cancer using mammographic images. Some of these methods require initial learning, and some of them do not require initial learning. As a major disadvantage of the trained methods, they require initial data for learning. Non-learning methods, such as clustering, also require knowledge of the number of clusters. This study used methods based on fractional partial differential equations for segmenting breast mammography images and then diagnosing cancer.Additionally, the proposed method of this study is a generalization of these methods in the field of fractional-order differential equations. To examine the performance of the proposed method in the present study, this method and some existing methods were simulated on 1000 sets of digital mammography images from the Digital Database for Screening Mammography (DDSM) belonging to the University of South Florida database. The output of the simulations indicated that the segmentation criteria were improved for the proposed method.