## 2 Related Works  
Fractional calculus has gained popularity in accomplishing several signal processing tasks as it serves to generalize some of the current system models that are based on integer-order derivatives. As a consequence, some scientists are working to incorporate FC into several engineering models, such as in digital controllers, digital filtering, and various image processing tasks, and then compare the performance of the resulting schemes to the previously achieved performance by conventional methods. Numerous image processing techniques rely on derivatives to gain valuable insights into image structures. Fractional derivatives, in particular, introduce an additional dimension of flexibility, which proves advantageous in performing tasks like edge detection. One can find several studies that confirm the advantages of FC-based models; we will discuss a few examples that particularly fall within the scope of this paper. [PERSON] [7] proposed an algorithm based on a fractional-order mask, which was used as the convolution kernel for edge enhancement. This method is characterized by its noise immunity and ability to detect edges in satellite and medical imaging; furthermore, the authors proved that their algorithm is suitable for real-time applications. [PERSON] et al. [8] proposed a fractional order edge detection method where they used an integral filter and a differential mask simultaneously for edge detection, allowing the extraction of targets with precise edges and complete structures in both noisy and noise-free images. [PERSON] et al. [9] proposed an algorithm to improve pixel contrast based on foreground and background gray levels by using the Riemann-Liouville fractional differential operator. Their proposed method controls the degree of contrast enhancement with the fractional differential order. [PERSON] et al. [10] proposed two general structures and a method for creating fractional masks; then, the components of these structures were evaluated using the fractional integral Atangana-Baleanu operator. Their results indicate that, with the proper choice of the fractional derivative order, this algorithm overcomes existing problems related to well-known masks such as Canny, Prewitt, and Sobel. Another example is a comprehensive image quality assessment metric proposed by [PERSON] [11], which evaluated both the overall alterations of an image by computing Grunwald-Letnikov derivatives and the localized alterations through image gradients. Additionally, they utilized visual saliency to prioritize changes in areas that are perceptually significant to the human visual system. To conclude the examples of the use of FC in image processing, [PERSON] et al. [12] reported extensive experiments on well-known benchmark image quality assessment databases; these results validate the effectiveness of their proposed approach. While existing research predominantly focuses on grayscale imagery, [PERSON] paper diverges by implementing and evaluating six fractional derivative-basededge detection algorithms tailored for color images. These algorithms encompass familiar techniques such as Canny, Sobel, Roberts, Laplacian, and Gaussian, as well as less common approaches, like the fractional-order robust edge detector (Contour Robuste d'Ordre Non Entier: CRONE) and fractional derivatives, showcasing their comparative performance. The following are a few examples that provide insight into the role and importance of edge filters in various practical scenarios that designers might find interest in. Innovative edge filters are important for image processing task applications. For example, [PERSON] and [PERSON] [13] compared modified Canny edge and Prewitt edge detection methods to evaluate their effectiveness in identifying bone fractures. Their study aimed to enhance the accuracy and specificity of diagnosing bone fractures by utilizing edge detection techniques.