This study investigates the problem of finite-time boundedness of a class of neural networks of Caputo fractional order with time delay and uncertain terms. New sufficient conditions are established by constructing suitable Lyapunov functionals to ensure that the addressed fractional-order uncertain neural networks are finite-time stable. Criteria for finite-time boundedness of the considered fractional-order uncertain models are also achieved. The obtained results are based on a newly developed property of Caputo fractional derivatives, properties of Mittag–Leffler functions and Laplace transforms. In addition, examples are developed to manifest the usefulness of our theoretical results.

Graph theory is one of the most essential parts in mathematics, where many practical problems are represented as different graphs and solved by graph-based algorithms. Among various techniques in graph theory, graph coloring is a widely used technique for solving real-world problems such as scheduling, security, waste management, image segmentation, register allocation, and puzzle-related problems. In this article, a novel fuzzy graph theory-based approach is proposed on image segmentation. Our proposed approach includes an improved optimal balanced histogram thresholding (IOBHT) method for gray-scale to binary image conversion, image representation based on fuzzy graph theory (FGT), and image segmentation using Widgerson’s coloring algorithm (WCA). This efficient image segmentation methodology is implemented in MATLAB and the experimental results from simulation shows that the proposed approach can minimize the computational time and improve the accuracy of image segmentation. Comparative analysis demonstrates that the proposed algorithm outperforms other existing algorithms.