Theory and Modern Applications
Page 38 of 98
The total variation model is widely used in image deblurring and denoising process with the features of protecting the image edge. However, this model usually causes some staircase effects. To overcome the sho...
In this paper, we derive seed and 1-soliton solutions of the Q2 equation in the Adler–Bobenko–Suris list. The seed solutions of Q2 are obtained using those of
...
The construction of backstepping control input needs the derivative of the virtual controller to be available. However, this requirement usually makes the implementation of the controller very difficult and co...
The dynamical behavior of the predator–prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementa...
Consider an anisotropic parabolic equation with a nonlinear convection term depending on the spatial variable. If the diffusion coefficients are degenerate, in general, the boundary trace cannot be defined for...
The purpose of this paper is to propose a semi-analytical technique convenient for numerical approximation of solutions of the initial value problem for p-dimensional delayed and neutral differential systems with...
In this paper we propose the balanced implicit numerical techniques for maintaining the nonnegative path of the solution in stochastic susceptible–infected–vaccinated–susceptible (SIVS) epidemic model. We can ...
In this paper, we consider the extended central factorial polynomials and numbers of the second kind, and investigate some properties and identities for these polynomials and numbers. In addition, we give some...
The existence of some class of multi-order nonlinear fractional systems is investigated in this paper. Some sufficient conditions of solutions for multi-order nonlinear systems are obtained based on fixed poin...
In this paper, two stochastic SIRS epidemic models with standard incidence were proposed and investigated. For the non-autonomous periodic model, the sufficient criteria for extinction of the disease are obtai...
In this paper, we investigate second order evolution differential equation in the frame of sequential conformable derivatives with nonlocal condition. First, we establish Duhamel’s formula in terms of a standa...
We deal with three important aspects of a generalized impulsive fractional order differential equation (DE) involving a nonlinear p-Laplacian operator: the existence of a solution, the uniqueness and the Hyers–Ul...
In this paper, we investigate a class of Hilfer fractional stochastic differential equations with nonlocal conditions. We first study the existence of mild solutions of these equations by means of stochastic a...
The class of quasi-convex functions contain all those finite convex functions which are defined on finite closed intervals of real line. The aim of this paper is to establish the bounds of the sum of left and ...
In this paper, we study a periodic model of hematopoiesis with a time-varying delay. Some new criteria are established to ensure that there are at least two positive periodic solutions by applying Krasnoselski...
Rossby waves, one of significant waves in the solitary wave, have important theoretical meaning in the atmosphere and ocean. However, the previous studies on Rossby waves commonly were carried out in the zonal...
This paper investigates a class of nonlinear dynamic integral inequalities with mixed nonlinearities in two independent variables. The obtained results can be utilized to study the boundedness of partial dynam...
The dynamical behavior of a discrete-time predator–prey model with modified Leslie–Gower and Holling’s type II schemes is investigated on the basis of the normal form method as well as bifurcation and chaos th...
In this study, we elucidated the exponential synchronization of a complex network system with time-varying delay. Then the exponential synchronization control of several types of complex network systems with t...
The present paper is aimed at studying the entropy of dynamical systems in product MV-algebras. First, by using the concept of logical entropy of a partition in a product MV-algebra introduced and studied by M...
In this study, we consider a predator–prey model with stage structure and anti-predator behavior such that the adult prey can counterattack their predators. We first investigate the existence and stability of ...
In this article, we discuss the sufficient conditions for the existence, uniqueness and stability of solutions to a class of nonlinear impulsive boundary value problem of fractional order differential equation...
In this paper, we offer an approach about the dissipativity of neutral-type memristive neural networks (MNNs) with leakage, additive time, and distributed delays. By applying a suitable Lyapunov–Krasovskii fun...
In this paper, we derive some sufficient conditions which ensure the existence and uniqueness of a solution for a class of nonlinear three point boundary value problems of fractional order implicit differentia...
We study almost periodic solutions for a class of nonlinear second-order differential equations involving reflection of the argument. We establish existence results of almost periodic solutions as critical poi...
In this paper, a predator–prey model with ratio-dependent and impulsive state feedback control is constructed, where the pest growth rate is related to an Allee effect. Firstly, the existence condition of the ...
In this paper, by means of a proper orthogonal decomposition (POD) we mainly reduce the order of the classical Crank–Nicolson finite difference (CCNFD) model for the fractional-order parabolic-type sine-Gordon...
Two modified exponential time differencing schemes based on the Fourier spectral method are developed to solve the 3-coupled nonlinear fractional Schrödinger equation. We compare the stability of the schemes b...
In this article, we propose a new method that determines an efficient numerical procedure for solving second-order fuzzy Volterra integro-differential equations in a Hilbert space. This method illustrates the ...
We represent general solution to a homogeneous linear difference equation of second order in terms of a specially chosen solution to the equation and apply it to get a representation of general solution to the...
In this paper, studies on the synchronization of fractional-order Takagi–Sugeno (T-S) fuzzy neural networks are performed. By employing a linear matrix inequality and constructing a skillful Lyapunov function,...
In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the second order neutral difference equation
...This paper is devoted to an investigation of a kind of p-Laplacian generalized Liénard equations with singularities of attractive and repulsive type, where the nonlinear term g has a singularity at the origin. Th...
We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to multi-point boundary conditions, under some assumptions on the nonlinearitie...
This paper develops a Legendre neural network method (LNN) for solving linear and nonlinear ordinary differential equations (ODEs), system of ordinary differential equations (SODEs), as well as classic Emden–F...
Fractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The actio...
This paper concerns the asymptotic behavior of the solution to a class of coupled semilinear parabolic systems with gradient terms. The Fujita-type blow-up theorems are established and the critical Fujita curv...
The main purpose of this study is to present an approximation method based on the Laguerre polynomials for fractional linear Volterra integro-differential equations. This method transforms the integro-differen...
For the pricing of vulnerable options, we improve the results of Klein and Inglis [Journal of Banking and Finance] and Tian et al. [The Journal of Futures and Markets], considering the circumstances in which t...
The construction of implicit Runge–Kutta–Nyström (RKN) method is considered in this paper. Based on the symmetric, symplectic, and exponentially fitted conditions, a class of implicit RKN integrators is obtain...
In this paper, we investigate the global threshold dynamics of a stochastic SIS epidemic model incorporating media coverage. We give the basic reproduction number
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In this paper, we present a stabilized lowest equal-order mixed finite element (FE) method for the Oseen viscoelastic fluid flow obeying an Oldroyd-B type constitutive law. To approximate the velocity, pressur...
In this paper, the investment process is modeled by backward stochastic differential equation. We investigate a necessary condition for optimal investment problem by the method of non-smooth analysis. Furtherm...
This paper is concerned with a class of two-term fractional differential equations. Three-point boundary value problems with mixed Riemann–Liouville fractional differential and integral boundary conditions are...
This article is devoted to the dynamical analysis of an explicit continuous iteration algorithm, describing its construction, relationship with the explicit trapezoid method, and error analysis. A theorem demo...
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