Many techniques have been recently employed by researchers to address the challenges posed by fractional differential equations. In this paper, we investigate the concept of Ulam-Hyers stability for a class of neutral fractional stochastic differential equations by using the Banach fixed point theorem and the stochastic analysis techniques. An example is presented at the end of the paper to show the interest and the applicability of the results.

Driver drowsiness is one of the leading causes of road accidents resulting in serious physical injuries, fatalities, and substantial economic losses. A sophisticated Driver Drowsiness Detection (DDD) system can alert the driver in case of abnormal behavior and avoid catastrophes. Several studies have already addressed driver drowsiness through behavioral measures and facial features. In this paper, we propose a hybrid real-time DDD system based on the Eyes Closure Ratio and Mouth Opening Ratio using simple camera and deep learning techniques. This system seeks to model the driver's behavior in order to alert him/her in case of drowsiness states to avoid potential accidents. The main contribution of the proposed approach is to build a reliable system able to avoid false detected drowsiness situations and to alert only the real ones. To this end, our research procedure is divided into two processes. The offline process performs a classification module using pretrained Convolutional Neural Networks (CNNs) to detect the drowsiness of the driver. In the online process, we calculate the percentage of the eyes' closure and yawning frequency of the driver online from real-time video using the Chebyshev distance instead of the classic Euclidean distance. The accurate drowsiness state of the driver is evaluated with the aid of the pretrained CNNs based on an ensemble learning paradigm. In order to improve models' performances, we applied data augmentation techniques for the generated dataset. The accuracies achieved are 97 % for the VGG16 model, 96% for VGG19 model and 98% for ResNet50 model. This system can assess the driver's dynamics with a precision rate of 98%.

The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed.