Theory and Modern Applications
Page 62 of 98
In this paper, we study the existence and uniqueness of the solution of stochastic differential equation by means of the properties of the associated condensing nonexpansive random operator. Moreover, by takin...
In this paper, a new mathematical modeling of rhizosphere microbial degradation with impulsive diffusion is proposed. By using the Floquet theorem, we find the rhizosphere microbe-eradication periodic solution...
In this paper, we continue the mathematical study started in (Jang et al. in J. Dyn. Differ. Equ. 16:297-320, 2004; Ni and Tang in Trans. Am. Math. Soc. 357:3953-3969, 2005) on the analytic aspects of the Lengyel...
This paper reports a novel Galerkin operational matrix of derivatives of some generalized Jacobi polynomials. This matrix is utilized for solving fourth-order linear and nonlinear boundary value problems. Two ...
In this paper, a stochastic cooperative predator-prey system with Beddington-DeAngelis functional response is proposed. By constructing Lyapunov functions, we demonstrate the existence of global positive solut...
This paper is concerned with the integral boundary value problems of higher-order fractional differential equation with. In the sense of a monotone homomorphism, some sufficient criteria are established to gua...
High-order compact difference schemes can achieve higher-order accuracy on uniform grids. However, in some cases these may not achieve the desired accuracy. Therefore, we propose a multigrid method based on hi...
A shifted Jacobi collocation method in two stages is constructed and used to numerically solve nonlinear Schrödinger equations (NLSEs) with a Kerr law nonlinearity, subject to initial-boundary conditions. An e...
In this paper, a collocation method based on Laguerre wavelets is proposed for the numerical solutions of linear and nonlinear singular boundary value problems. Laguerre wavelet expansions together with operat...
In this paper, sufficient conditions are established for the forced oscillation of fractional partial differential equations of the form
We consider two-dimensional predator-prey systems with Beddington-DeAngelis-type functional response on periodic time scales. For this special case, we try to find the necessary and sufficient conditions for t...
In this paper, we find formulas of general solution for a kind of impulsive differential equations with Hadamard fractional derivative of order
In this paper, the effect of the two different delays on the dynamics of a three-species ratio-dependent predator-prey food-chain model is considered. By regarding the delay as the bifurcation parameter, the l...
In this work, we consider the delta shape operator of a surface parameterized by the product of two arbitrary time scales. In particular, we present a matrix representation of the delta shape operators with re...
By means of the method of upper and lower solutions together with the Schauder fixed point theorem, the conditions for the existence of at least one positive solution are established for some higher-order sing...
By Kranoselskii’s fixed point theorem, we state some sufficient conditions of the existence of nonoscillatory solutions tending to zero as
In this work, we use a reproducing kernel method for investigating the sine-Gordon equation with initial and boundary conditions. Numerical experiments are studied to show the efficiency of the technique. The ...
The Camassa-Holm equation, a completely integrable evolution equation, contains rich geometric structures. For the existence of the bi-Hamiltonian structure and the so-called peaked wave solutions, considerabl...
An age-structured in-host viral infection model with humoral immunity, consisting of partial differential and ordinary differential equations, is investigated. By calculation we get the basic reproduction number
This paper studies the exponential stability problem for a class of networked control systems (NCSs) with time delays and packet dropouts. By considering the disturbed state-feedback controller, the closed-loo...
We present several numerical schemes for computing the unitary polar factor of rectangular complex matrices. Error analysis shows high orders of convergence. Many experiments in terms of number of iterations a...
The paper considers the problem of exponential stability and convergence rate to solutions of perturbed linear discrete homogeneous systems. New criteria on exponential stability are derived by using the secon...
A nonautonomous discrete competitive system with nonlinear inter-inhibition terms and one toxin producing species is studied in this paper. Sufficient conditions which guarantee the extinction of one of the co...
Departing from a finite-difference scheme to approximate the solutions of the Burgers-Huxley equation, the present manuscript extends that technique to higher dimensions. We show that our methodology possesses...
In this paper, we use a fixed point principle regarding a condensing mapping with some measure of noncompactness. We assume there is no compactness assumption, and we give sufficient conditions for the existen...
In the present paper, the positivity of a multi-dimensional difference operator in the half-space is considered. The structure of fractional spaces generated by this operator is investigated. The equivalence o...
We consider a class of higher-order nonlinear Riemann-Liouville fractional differential equation with Riemann-Stieltjes integral boundary value conditions and impulses as follows:
In this article, a mathematical model of a rotavirus infection incorporating vaccination has been developed and comprehensively analyzed. The basic reproduction number,
...
In this paper, we consider the biharmonic problem of a partial differential inclusion with Dirichlet boundary conditions. We prove existence theorems for related partial differential inclusions with convex and...
In this paper, we investigate the existence of multiple solutions for a class of ordinary differential systems with min-max terms. We present two fundamental results for the existence of solutions. An illustra...
This paper is concerned with controlled nonlinear impulsive evolution equations with nonlocal conditions. The existence of PC-mild solutions is proved, but the uniqueness cannot be obtained. By constructing ap...
In this paper, we consider the fractional modified Zakharov system with a quantum correction. This system can be regarded as a generalization of the Garcia model to the fractional order. By the properties of t...
This paper is concerned with the long-time behavior of solutions to the weakly damped wave equation with lower regular forcing defined on the entire space
...
In this paper, we study the existence and uniqueness of solutions for a problem consisting of nonlinear Langevin equation of Riemann-Liouville type fractional derivatives with the nonlocal Katugampola fraction...
In this paper the second-order random fuzzy differential equations (SRFDEs) under generalized Hukuhara differentiability are introduced. Under suitable conditions we obtain the existence and uniqueness results...
In this manuscript, we work to actualize the Darbo (Banas and Goebel in Measure of Noncompactness in Banach Space. Lecture Notes in Pure and Applied Mathematics, 1980) fixed point theorem (FPT) coupled with the H...
In this paper, a class of Nicholson-type delay systems with impulsive effects is considered. First, an equivalence relation between the solution (or positive periodic solution) of a Nicholson-type delay system...
In this paper, we consider the initial boundary value problem for a coupled fractional diffusion system. By using eigenfunction expansions and a priori estimates, we establish the existence and uniqueness of t...
To solve the stiff stochastic differential equations, we propose an improved Milstein method, which is constructed by adding an error correction term to the Milstein scheme. The correction term is derived from...
In the present paper, by using the theory of semigroup operators and the Schauder fixed point theorem, we define the mild solution of a fractional partial differential equation and obtain the existence and uni...
In this article we present a new fixed point theorem for a class of generalized concave operators and we establish some properties of positive solutions for the operator equation ...
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