In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using the (...) classical technique of functional analysis. At the end, the results are verified with the help of examples. (shrink)

The quality and quantity of training data are crucial to the performance of a deep-learning-based brain-computer interface system. However, it is not practical to record EEG data over several long calibration sessions. A promising time- and cost-efficient solution is artificial data generation or data augmentation. Here, we proposed a DA method for the motor imagery EEG signal called brain-area-recombination. For the BAR, each sample was first separated into two ones by left/right brain channels, and the artificial samples were generated by (...) recombining the half-samples. We then designed two schemas corresponding to the single- and multi-subject scenarios. Extensive experiments using the classifier of EEGnet were conducted on two public datasets under various training set sizes. In both schemas, the BAR method can make the EEGnet have a better performance of classification. To make a comparative investigation, we selected two common DA methods, and the BAR method beat them. Further, using the proposed BAR for augmentation, EEGnet achieved up to 8.3% improvement than a typical decoding algorithm CSP-SVM, note that both the models were trained on the augmented dataset. This study shows that BAR usage can significantly improve the classification ability of deep learning to MI-EEG signals. To a certain extent, it may promote the development of deep learning technology in the field of BCI. (shrink)