Traditional computer vision techniques aim to extract meaningful information from images but often depend on manual feature engineering, making it difficult to handle complex real-world scenarios. Fractional calculus (FC), which extends derivatives to non-integer orders, provides a flexible way to model systems with memory effects and long-term dependencies, making it a powerful tool for capturing fractional rates of variation. Recently, neural networks (NNs) have demonstrated remarkable capabilities in learning complex patterns directly from raw data, automating computer vision tasks and enhancing performance. Therefore, the use of fractional calculus in neural network-based computer vision is a powerful method to address existing challenges by effectively capturing complex spatial and temporal relationships in images and videos. This paper presents a survey of fractional calculus neural network-based (FC NN-based) computer vision techniques for denoising, enhancement, object detection, segmentation, restoration, and NN compression. This survey compiles existing FFC NN-based approaches, elucidates underlying concepts, and identifies open questions and research directions. By leveraging FC’s properties, FC NN-based approaches offer a novel way to improve the robustness and efficiency of computer vision systems.

In this article, we aim to extend the firefly algorithm (FA) to solve bound constrained mixed-integer nonlinear programming (MINLP) problems. An exact penalty continuous formulation of the MINLP problem is used. The continuous penalty problem comes out by relaxing the integrality constraints and by adding a penalty term to the objective function that aims to penalize integrality constraint violation. Two penalty terms are proposed, one is based on the hyperbolic tangent function and the other on the inverse hyperbolic sine function. We prove that both penalties can be used to define the continuous penalty problem, in the sense that it is equivalent to the MINLP problem. The solutions of the penalty problem are obtained using a variant of the metaheuristic FA for global optimization. Numerical experiments are given on a set of benchmark problems aiming to analyze the quality of the obtained solutions and the convergence speed. We show that the firefly penalty-based algorithm compares favourably with the penalty algorithm when the deterministic DIRECT or the simulated annealing solvers are invoked, in terms of convergence speed.