Breast cancer has become increasingly prevalent and has shown a significant rise in recent years, highlighting the urgent need for effective models for classification and digital diagnosis. Challenges in this research include the absence of lightweight models with augmented data, motivating us to explore new approaches. This paper presents a Fractional Convolutional Neural Network (Fractional CNN) model for the classification of benign and malignant tissue slides of breast cancer. Our results demonstrate that the Fractional CNN achieved a higher accuracy, approximately 91%, for one type of magnification within the dataset compared to the Conventional Convolutional Neural Network. This indicates the potential of the Fractional CNN in improving diagnostic accuracy for breast cancer.