Theory and Modern Applications
Page 37 of 98
Until now, the theories about the convergence analysis, the almost surely and mean square exponential stability of the numerical solution for neutral stochastic functional differential equations with Markovian...
This paper focuses on the Caputo fractional differential system involving coupled integral boundary conditions and parameters. Using the properties of the Green function, the Leray–Schauder’s alternative and t...
The phytoplankton–zooplankton is fundamentally important to study plankton and protect marine environment. In this paper, we propose a diffusive phytoplankton–zooplankton model, in which we also consider time ...
This paper is devoted to investigating the dynamics of a diffusive Leslie–Gower predator–prey system with ratio-dependent Holling III functional response. We first establish the stability of positive constant ...
In this paper, a high-order numerical scheme is proposed for solving the two-dimensional fractional reaction–subdiffusion equation. The method is based on adopting a third-order weighted and shifted Grünwald d...
In this paper, the concept of upper and lower solutions method combined with the fixed point theorem is used to investigate the existence of oscillatory and nonoscillatory solutions for a class of initial valu...
Representations of general solutions to three related classes of nonlinear difference equations in terms of specially chosen solutions to linear difference equations with constant coefficients are given. Our r...
In this paper, we consider the flocking problem for a discrete Cucker–Smale model with packet loss. For describing the packet loss process, a more general condition including four different cases is adopted in...
The Caputo fractional version of the generalized Newell–Whitehead–Segel model is considered. We introduced a numerical scheme to solve analytically the proposed application. We updated the style of the general...
The exact solutions of the Riemann problem for a symmetric system of Keyfitz–Kranzer type are obtained in fully explicit forms. Furthermore, the global solutions of the double Riemann problems are also constru...
In this paper, for a class of linear networked iterative learning control (ILC) systems, methods to compensate dropped input data in time or iteration domain are compared. Specifically, the transition matrices...
In this paper, we introduce a new numerical method for pricing American-style options, which has long been considered as a very challenging problem in financial engineering. Based on the HODIE (high order via ...
In this paper, the implicit midpoint method is presented for solving Riesz tempered fractional diffusion equation with a nonlinear source term, where the tempered fractional partial derivatives are evaluated b...
In this paper, local stability and Hopf bifurcation of a delayed heroin model with saturated treatment function are discussed. First of all, sufficient conditions for local stability and existence of Hopf bifu...
In this paper, quaternion-valued fuzzy cellular neural networks (QVFCNNs) with time-varying delays are considered. First, we decompose QVFCNNs into their equivalent real-valued systems according to Hamilton’s ...
So far, there are no any publications for solving and obtaining a numerical solution of Volterra integro-differential equations in the complex plane by using the finite element method. In this work, we use the...
The dynamics of the osteoporotic bone turnover is studied in this paper with the aid of stability analysis of the associated mathematical model. Osteoporosis, which is a common bone disorder, is studied in thi...
In this paper, the diffraction problem of periodic strip gratings is considered. The previous study of this problem usually concentrated on the numerical method; however, we try to analyze this problem and the...
For discrete-time iterative learning control systems, the discrete Fourier transform (DFT) is a powerful technique for frequency analysis, and Toeplitz matrices are a typical tool for the system input–output t...
In this paper, we mainly give the Lie algebras E, F and H of three kinds and their commutator, respectively. Next, we establish three isospectral problems with the help of their corresponding loop algebras Ẽ, F̃,...
In this paper we develop the existence theory for a nonlinear Langevin equation involving Caputo fractional derivatives of different orders and Riemann–Liouville fractional integral supplemented with nonlocal ...
The primary motivation of this paper is to extend the application of the reproducing-kernel method (RKM) and the residual power series method (RPSM) to conduct a numerical investigation for a class of boundary...
Any random model represents an action where uncertainty is present. In this article, we investigate a random process solution of the random convection–diffusion model using the finite difference technique. Add...
In this paper, the robust optimal filtering problem is discussed for time-varying networked systems with randomly occurring quantized measurements via the variance-constrained method. The stochastic nonlineari...
This paper we devote to considering the periodic problem for the impulsive evolution equations with delay in Banach space. By using operator semigroup theory and the fixed point theorem, we establish some new ...
In this paper, we present results on the existence, uniqueness, and Ulam–Hyers–Mittag-Leffler stability of solutions to a class of ψ-Hilfer fractional-order delay differential equations. We use the Picard operato...
In this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov–Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonli...
This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of...
In this paper, we suggest a new exponential implicit method based on full step discretization of order four for the solution of quasilinear elliptic partial differential equation of the form ...
We investigate the existence and uniqueness of a solution for a Sturm–Liouville fractional differential equation with a multi-point boundary condition via the Caputo derivative; existence and uniqueness result...
This paper is concerned with the random exponential attractor for second order non-autonomous stochastic lattice system with multiplicative white noise and unbounded nonlinearity. Firstly, we transfer the stoc...
This paper is concerned with a reaction-diffusion predator–prey model with prey-taxis and intraguild predation. We first discuss the basic properties of solutions with the aid of differential equation theory. ...
In this paper, we study the following Lotka–Volterra commensal symbiosis model of two populations with Michaelis–Menten type harvesting for the first species:
...In this paper, we study a stage-structured predator–prey model incorporating refuge for prey and additional food for predator. By analyzing the corresponding characteristic equations, we investigate the local ...
In this paper, considering the impact of stochastic environment noise on infection rate, a stochastic SIS epidemic model with nonlinear incidence rate is proposed and analyzed. Firstly, for the corresponding d...
In this paper, we obtain sufficient conditions for the nonexistence of global solutions for some classes of q-difference inequalities. Our approach is based on the weak formulation of the problem, a particular ch...
In a recent paper several periodic systems of difference equations have been presented. We show in an elegant way that all the results therein follow from some known ones. We also show how some extensions of t...
In this paper, we study the uniqueness of solutions for a fractional differential equation with dependence on the first order derivative. By means of Banach’s contraction mapping principle and a weighted norm ...
We study an epidemic model with nonlinear incidence rate, describing the saturated mass action and the psychological effect of certain serious diseases on the community. Firstly, the existence and local stabil...
In this paper, we study the nonlocal boundary value problem for a nonlinear fractional differential coupled system with fractional order impulses. Applying Nonlinear Alternative of Leray–Schauder, we obtain so...
It is well known that the drug treatment is always combined with the injection of immune factors. In this paper, a virus infection model with state-dependent impulsive control is considered. Firstly, by derivi...
This paper pursues an adaptive fuzzy control scheme for a class of nonlinear systems with stochastic switching. A general controller and adaptive mechanism are designed by utilizing Lyapunov function approach ...
This article represents a numerical analysis for a stochastic dengue epidemic model with incubation period of virus. We discuss the comparison of solutions between the stochastic dengue model and a determinist...
Dengue is one of the important infectious diseases in the world. In Malaysia, dengue occurs nationally and has been endemic for more than a decade. Hence, the modeling of dengue transmission is of great import...
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