This research paper introduces a novel mathematical model that integrates fractional calculus with topological data analysis (TDA) for image segmentation. Fractional calculus, which extends the concept of derivatives and integrals to arbitrary orders, effectively addresses the non-local and hereditary properties of images, capturing textures and patterns across various scales and complexities. TDA, utilizing robust tools for identifying shape and connectivity features, complements this by capturing intricate topological characteristics often overlooked by traditional segmentation methods. Leveraging persistent homology, a core concept in TDA, the model classifies, and segments image regions based on their topological features, which remain invariant under deformations such as bending and stretching. This integrated approach aims to enhance the accuracy and reliability of image segmentation, offering a significant advancement over existing methods.