Theory and Modern Applications
Page 31 of 98
The interaction between prey and predator is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of predator and prey interaction with non-ove...
This research demonstrates the log-convexity and log-concavity of the modified Bessel function of the first kind and the related functions. The method of coefficient is used to verify such properties. One of o...
In this study, we have proposed an efficient numerical algorithm based on third degree modified extended B-spline (EBS) functions for solving time-fractional diffusion wave equation with reaction and damping t...
This paper deals with the model of fractional HIV-1 infection of CD4+T cells transformation with homogeneous Neumann boundary conditions. Numerical methods for solving fractional time differential equations are d...
Recently, spaces of ideal convergent sequences of bounded linear operators were studied by Khan et al. (Numer. Funct. Anal. Optim. 39:1278-1290, 2018). This has motivated us to propose the intuitionistic fuzzy I-...
In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality...
Under simple conditions on f and a, we show the existence of positive radial solutions for the n-dimensional elliptic differential system
This paper is concentrated on a class of difference equations with a Weyl-like fractional difference in a Banach space X forms like
In this paper, by introducing the fractional derivatives in the sense of Caputo, the modified general mapping deformation method (MGMDM) and the modified fractional variational iteration method (MFVIM) are app...
In this paper, a prey-predator model with Allee effect and Holling type-I functional response is established, and its dynamical behaviors are studied in detail. The existence, boundedness and stability of the ...
Pulse vaccination is a repeated vaccination policy, which plays a tremendous role in the global fight against communicable diseases in terms of saving medical resources and decreasing the economic burden. In t...
The fractional sub-diffusion equation, which is obtained by replacing the time derivative in ordinary diffusion by a fractional derivative of order ϑ with
...
After publication of this article [1], it was brought to our attention that the article type should be “Research” rather than “Review”.
The original article was published in Advances in Difference Equations 2019 2019:214
A finite difference scheme based on extended cubic B-spline method for the solution of time fractional telegraph equation is presented and discussed. The Caputo fractional formula is used in the discretization...
In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
In this paper, we identify a weak focus with order up to 3 for a Leslie–Gower prey–predator model with three parameters. The known work computed the first Lyapunov quantity and discussed Hopf bifurcations of t...
In this paper, a class of sixth-order finite difference schemes for the Helmholtz equation with inhomogeneous Robin boundary condition is derived. This scheme is based on the sixth-order approximation for the ...
Liouville–Green (WKB) asymptotic approximations are constructed for some classes of linear second-order difference equations. This is done starting from certain “canonical forms” for the three-term linear recurre...
This paper studies a stochastic predator–prey model for integrated pest management. It shows that the system has a positive solution that exists globally. The long time behavior of the system is investigated, ...
A Lotka–Volterra predator–prey model incorporating predator cannibalism is proposed and studied in this paper. The existence and stability of all possible equilibria of the system are investigated. Our study s...
We deal with Nicholson’s blowflies model with proportional delays. Employing the differential inequality theory, we give a new sufficient condition that guarantees the exponential convergence of all solutions ...
In this paper, we perform a further investigation of the Gegenbauer polynomials, the Chebyshev polynomials of the first and second kinds and the Legendre polynomials. By making use of some analytic and combina...
In this paper, we consider the existence and global exponential stability of pseudo almost automorphic solutions to quaternion-valued cellular neural networks with infinitely distributed delays. Unlike most pr...
Focusing on delay differential neoclassical growth model in random environments, we introduce the stochastic model to describe the dynamics of the long-run behavior of the economy with a parameter perturbed by...
In this paper, a new kind of conformable fractional derivative on arbitrary time scales is introduced. The basic conformable derivative rules are proved. We introduce a new definition of exponential functions,...
This paper is concerned with almost sure exponential stabilization of neural networks by intermittent control based on delay observations. By the stochastic comparison principle and Itô’s formula, a sufficient...
This paper is to investigate the finite-time synchronization of stochastic Markovian jumping genetic oscillator networks with time-varying delay and Lévy noise. At first, we generalize the finite-time stabilit...
In this paper, we study the existence of positive solutions for boundary value problems of high-order conformable differential equations involving the p-Laplacian operator. By applying properties of the Green’s f...
In this work, we study the numerical approximation for the space fractional FitzHugh–Nagumo model. The numerical scheme is based on the Crank–Nicolson (C–N) method in time and Legendre-spectral method in space...
In this paper, the existence of a positive solution to a boundary value problem of fractional differential equations with the p-Laplacian operator is studied. By applying a monotone iterative method, some existen...
In this paper, we consider the optimal control problem for the mean-field stochastic differential equations with delay and state constraint. By virtue of the classical Ekeland’s variational principle, the dual...
Environmental fluctuations and toxin-producing phytoplankton are crucial factors affecting marine ecosystems. In this paper, we propose a stochastic phytoplankton-toxin phytoplankton–zooplankton model to study...
Multistability, i.e., coexisting attractors, is one of the most exciting phenomena in dynamical systems. This paper presents a new category of coexisting hidden attractor: five-dimensional (5D) systems with a ...
In the present paper, we firstly improve the results on traveling wave solution that were established in (Liu and Weng in J. Differ. Equ. 258:3688–3741, 2015) for a neutral reaction–diffusion equation with quasi-...
In this paper the asymptotic stability is concerned for a class of neutral delay differential-algebraic equations (NDDAEs). We will present two criteria by evaluating a corresponding harmonic function on the b...
This paper studies the transient slip flow and heat transfer of a fluid driven by the oscillatory pressure gradient in a microchannel of elliptic cross section. The boundary value problem for the thermal-slip ...
In this paper, the combination of efficient sixth-order compact finite difference scheme (E-CFDS6) based proper orthogonal decomposition and Strang splitting method (E-CFDS6-SSM) is constructed for the numeric...
A new constructive method for the finite-difference solution of the Laplace equation with the integral boundary condition is proposed and justified. In this method, the approximate solution of the given proble...
This paper addresses exponential basis and compact formulation for solving three-dimensional convection-diffusion-reaction equations that exhibit an accuracy of order three or four depending on exponential exp...
In this paper, our aim is to investigate the region stability of stochastic discrete time-delay systems. Firstly, region stabilities of systems are defined by a spectrum operator. Secondly, with the aid of lin...
This paper is committed to studying adaptive control design of Mittag-Leffler stabilization and synchronization for delayed fractional-order bidirectional associative memory (BAM) neural networks. Considering ...
In this paper, we prove some new generalizations of dynamic Opial-type inequalities on time scales. From these inequalities, as special cases, we formulate some integral and discrete inequalities proved in the...
In the paper, we are concerned with the existence of periodic solutions for a coupled Rayleigh system. By combining graph theory with coincidence degree theory as well as Lyapunov function method, two new suff...
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