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Fractional calculus and fractional processes are research areas that are gaining increasing attention, with applications in control systems and image processing. Fractional-order systems are a natural generalization of classical integer-order systems with the ability to accurately model a wide range of real-world physical systems. The fusion and noise suppression of medical images in image processing are essential, as these techniques provide valuable information to support clinical diagnosis and treatment. Image fusion is a significant factor in image processing due to the increase in image acquisition models. Recently, fractional operators have gained importance in image processing. Additionally, powerful fractional operating tools have been introduced, offering extensive applications in the analysis and design of nonlinear control systems. Singular systems are governed by singular differential equations, endowing the systems with many special features not found in classical systems. Fractional-order control systems, which draw from integer-order control systems, are drawing increasing attention within the field.