Fractional SEIR model and data-driven predictions of COVID-19 dynamics of Omicron variant.

We study the dynamic evolution of COVID-19 caused by the Omicron variant via a fractional susceptible-exposed-infected-removed (SEIR) model. Preliminary data suggest that the symptoms of Omicron infection are not prominent and the transmission is, therefore, more concealed, which causes a relatively slow increase in the detected cases of the newly infected at the beginning of the pandemic. To characterize the specific dynamics, the Caputo-Hadamard fractional derivative is adopted to refine the classical SEIR model.

Finite-time stability analysis of fractional differential systems with variable coefficients.

In this paper, we study finite-time stability of fractional differential systems with variable coefficients, which includes the homogeneous and nonhomogeneous delayed cases. Based on the theories of fractional differential equations, we obtain three theorems on the finite-time stability, which give some sufficient conditions on finite-time stability, respectively, for homogeneous systems without and with time delay and for the nonhomogeneous system with time delay.

Approximation to Hadamard Derivative via the Finite Part Integral.

In 1923, Hadamard encountered a class of integrals with strong singularities when using a particular Green's function to solve the cylindrical wave equation. He ignored the infinite parts of such integrals after integrating by parts. Such an idea is very practical and useful in many physical models, e.

Synchronization of fractional fuzzy cellular neural networks with interactions.

In this paper, we introduce fuzzy theory into the fractional cellular neural networks to dynamically enhance the coupling strength and propose a fractional fuzzy neural network model with interactions. Using the Lyapunov principle of fractional differential equations, we design the adaptive control schemes to realize the synchronization and obtain the synchronization criteria. Finally, we provide some numerical examples to show the effectiveness of our obtained results.

Impulsive synchronization of fractional Takagi-Sugeno fuzzy complex networks.

This paper focuses on impulsive synchronization of fractional Takagi-Sugeno (T-S) fuzzy complex networks. A novel comparison principle is built for the fractional impulsive system. Then a synchronization criterion is established for the fractional T-S fuzzy complex networks by utilizing the comparison principle.

Preface: Recent Advances in Fractional Dynamics.

This Special Focus Issue contains several recent developments and advances on the subject of Fractional Dynamics and its widespread applications in various areas of the mathematical, physical, and engineering sciences.

Determination of coefficients of high-order schemes for Riemann-Liouville derivative.

Although there have existed some numerical algorithms for the fractional differential equations, developing high-order methods (i.e., with convergence order greater than or equal to 2) is just the beginning.

Equivalent system for a multiple-rational-order fractional differential system.

The equivalent system for a multiple-rational-order (MRO) fractional differential system is studied, where the fractional derivative is in the sense of Caputo or Riemann-Liouville. With the relationship between the Caputo derivative and the generalized fractional derivative, we can change the MRO fractional differential system with a Caputo derivative into a higher-dimensional system with the same Caputo derivative order lying in (0,1). The stability of the zero solution to the original system is studied through the analysis of its equivalent system.

Chaos synchronization in fractional differential systems.

This paper presents a brief overview of recent developments in chaos synchronization in coupled fractional differential systems, where the original viewpoints are retained. In addition to complete synchronization, several other extended concepts of synchronization, such as projective synchronization, hybrid projective synchronization, function projective synchronization, generalized synchronization and generalized projective synchronization in fractional differential systems, are reviewed.

On the bound of the Lyapunov exponents for the fractional differential systems.

In recent years, fractional(-order) differential equations have attracted increasing interests due to their applications in modeling anomalous diffusion, time dependent materials and processes with long range dependence, allometric scaling laws, and complex networks. Although an autonomous system cannot define a dynamical system in the sense of semigroup because of the memory property determined by the fractional derivative, we can still use the Lyapunov exponents to discuss its dynamical evolution. In this paper, we first define the Lyapunov exponents for fractional differential systems then estimate the bound of the corresponding Lyapunov exponents.

Outer synchronization of coupled discrete-time networks.

In this paper, synchronization between two discrete-time networks, called "outer synchronization" for brevity, is theoretically and numerically studied. First, a sufficient criterion for this outer synchronization between two coupled discrete-time networks which have the same connection topologies is derived analytically. Numerical examples are also given and they are in line with the theoretical analysis.

Synchronization between two coupled complex networks.

We study synchronization for two unidirectionally coupled networks. This is a substantial generalization of several recent papers investigating synchronization inside a network. We derive analytically a criterion for the synchronization of two networks which have the same (inside) topological connectivity.

On the bound of the Lyapunov exponents for continuous systems.

In this paper, both upper bounds and lower bounds for all the Lyapunov exponents of continuous differential systems are determined. Several examples are given to show the application of the estimates derived here.

Estimating the Lyapunov exponents of discrete systems.

In the present paper, our aim is to determine both upper and lower bounds for all the Lyapunov exponents of a given finite-dimensional discrete map. To show the efficiency of the proposed estimation method, two examples are given, including the well-known Henon map and a coupled map lattice.