Due to the alarming rise in types of crime committed and the number of criminal activities across the world, there is a great need to amend the existing policies and models adopted by jurisdictional institutes. The majority of the mathematical models have not included the history of the crime committed by the individual, which is vital to control crime transmission in stipulated time. Further, due to various external factors and policies, a considerable number of criminals have not been imprisoned. To address the aforementioned issues prevailing in society, this research proposes a fractional-order crime transmission model by categorizing the existing population into four clusters. These clusters include law-abiding citizens, criminally active individuals who have not been imprisoned, prisoners, and prisoners who completed the prison tenure. The well-posedness and stability of the proposed fractional model are discussed in this work. Furthermore, the proposed model is extended to the delayed model by introducing the time-delay coefficient as time lag occurs between the individual’s offense and the judgment. The endemic equilibrium of the delayed model is locally asymptotically stable up to a certain extent, after which bifurcation occurs.
Deep Learning is considered one of the most effective strategies used by hedge funds to maximize profits. But Deep Neural Networks (DNN) lack theoretical analysis of memory exploitation. Some traditional time series methods such as Auto-Regressive Integrated Moving Average (ARIMA) and Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) work only when the entire series is pre-processed or when the whole data is available. Thus, it fails in a live trading system. So, there is a great need to develop techniques that give more accurate stock/index predictions. This study has exploited fractional-order derivatives’ memory property in the backpropagation of LSTM for stock predictions. As the history of previous stock prices plays a significant role in deciding the future price, fractional-order derivatives carry the past information along with itself. So, the use of Fractional-order derivatives with neural networks for this time series prediction is meaningful and helpful.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.