Using the fractional order method to generalize strengthening buffer operator and weakening buffer operator

This study proposes to use the fractional-order accumulation grey model (FGM) combined with the fractional-order buffer operator to predict the cumulative confirmed cases in different stages of COVID-19. In the early stages of COVID-19 outbreak, when the cumulative confirmed cases increased rapidly, we used the strengthening buffer operator in the prediction process. After the government’s prevention measures started to take effect, the growth rate of cumulative confirmed cases slows down. Therefore, the weakening buffer operator is applied in the prediction process. The fractional order of the buffer operator is derived from the historical data, which are more relevant. The empirical analysis of seven countries’ data shows that the FGM with the fractional-order buffer operator achieves the best results for most cases. The fractional-order buffer operator improves the prediction accuracy of the FGM in this study. Our study also suggests a practical way for predicting the trend of epidemic diseases.

“…is transform would be conducive to accurate prediction. Wu et al [24] extended the traditional integer-order buffer operator to the fractional-order one. Definition 3.…”

Section: Methodsmentioning

confidence: 99%

“…is means that the buffer operators they built may have the problem of poor versatility. Recently, Wu et al [24] generalized the expression of weakening and strengthening buffer operators using the fractional order, which provides us a new choice to generate different buffer operators based on different fractional orders.…”

Section: Introductionmentioning

confidence: 99%

Forecasting the Cumulative Confirmed Cases with the FGM and Fractional-Order Buffer Operator in Different Stages of COVID-19

Chen

Zhang

et al. 2021

“…e neural network has the unique knowledge representation structure and can process information, learn, and adapt to the unknown system efficiently and quickly, which provide new research ideas for control problems and intelligent information processing. Integer order differential equations cannot describe the memory properties of neurons and the dependence on past history, but the fractional-order calculus [1][2][3][4], which has strong memory and hereditary characteristic, contains all of the information from the start point to the current moment and can describe the memory properties and dynamical behaviors of neurons more accurately. erefore, FNNs can improve the computational ability of neurons, speed up the information transmission of neurons, and solve the problem of parameter identification effectively.…”

Section: Introductionmentioning

confidence: 99%

Sliding Mode Matrix-Projective Synchronization for Fractional-Order Neural Networks

Lei

Jiang

2021

This work generalizes the projection scaling factor to a general constant matrix and proposes the matrix-projection synchronization (MPS) for fractional-order neural networks (FNNs) based on sliding mode control firstly. This kind of scaling factor is far more complex than the constant scaling factor, and it is highly variable and difficult to predict in the process of realizing the synchronization for the driving and response systems, which can ensure high security and strong confidentiality. Then, the fractional-order integral sliding surface and sliding mode controller for FNNs are designed. Furthermore, the criterion for realizing MPS is proved, and the reachability and stability of the synchronization error system are analyzed, so that the global MPS is realized for FNNs. Finally, a numerical application is given to demonstrate the feasibility of theory analysis. MPS is more general, so it is reduced to antisynchronization, complete synchronization, projective synchronization (PS), and modified PS when selecting different projective matrices. This work will enrich the synchronization theory of FNNs and provide a feasible method to study the MPS of other fractional-order dynamical models.

“…e fractional calculus is a name for the theory of integrals and derivatives of arbitrary order, which unifies and generalizes the notions of integer-order differential and integral [1]. e idea of fractional calculus is known in developing regular calculation referring to Leibniz and L'hospital's work in 1695 [2].…”

Section: Introductionmentioning

confidence: 99%

A Bibliometric Analysis and Visualization of Fractional Order Research in China over Two Decades (2001–2020)

Yang

Xue

et al. 2021

Fractional order research has interdisciplinary characteristics and has been widely used in the field of natural sciences. Therefore, fractional order research has become an important area of concern for scholars. This paper used 2854 literatures collected from China National Knowledge Infrastructure (CNKI) database from 2001 to 2020 as the data source and used bibliometrics and two visualization methods to conduct bibliometric analysis and visualization research on China’s fractional order research. To begin with, this paper analyzed the time series distribution of publications, the distribution of research institutions, the author cooccurrence network, the distribution of important journals, and the distribution of important literature, which explained the research status of the fractional order. Furthermore, this paper used VOSviewer software to analyze the clustering and density distribution of the fractional order research keywords, which revealed the hotspots of the fractional order research. Finally, with the help of CiteSpace software, the burst keywords were analyzed to further explore the frontiers of fractional order research. This paper systematically reveals the research status, research hotspots, and research frontiers of China’s fractional order research, which can provide certain theoretical and practical references for related follow-up researchers.