This paper deals with the asymptotical stability of singular LPV linear systems with time delay. By using a new method to deal with nonlinear terms, sufficient conditions for asymptotical stability of nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique.

In this paper, we investigate unique nontrivial solution for a class nonlinear boundary value problem with fractional q-derivative where$D_{q}^{\alpha}$are fractional q-derivative of Riemann-Liouville type,$b \geq 0, \beta \geq 0$. Based on the fixed point theorems for increasing$\varphi-(h, e)$-concave operators, we establish some sufficient conditions for the existence and uniqueness of nontrivial solution of the problem; on the other hand, an iterative scheme is constructed for approximating the nontrivial solution.

In this paper, the existence and nonexistence of solutions for a class of fractional differential equations are studied by using an interesting fixed point theorem on order intervals and the well-known Schauder's fixed point theorem. The theorems generalize some existing results on this topic.

The purpose of this paper is to discuss the existence and uniqueness of positive solutions for fractional differential equations with infinite-point boundary value conditions where$D_{0+}^{\alpha}$is the standard Riemann-Liouville derivative of order$\alpha, \alpha > 2, n-1 < \alpha\leq n,j\in[1, n-2]$is a fixed integer,$0 < \beta < \alpha-1, \eta_{j}\in R, 0 < \xi_{1} < \xi_{2} < \ldots < \xi_{j-1} < \xi_{j} <$…$< 1(j=1,2,\ldots), \sum^{\infty}_{j=1}\eta_{j}\xi^{\alpha-\beta-1}_{j} \neq1$. By means of fixed point theorems for mixed monotone operator with perturbation, some existence and uniqueness results of positive solutions are obtained.

The dynamic behavior research of infectious dis-ease models has always been a very important branch of biomathematics research. Since the outbreak of COVID-19 in December 2019, many scholars have formulated and evaluated prevention and control strategies by establishing mathematical models of their dynamics to understand the mechanism of epidemic diseases. And the impact of media information on infectious diseases is obvious. In this paper, a class of SIRSM models with the influence of positive media information are established, and the feasible domain of system dynamic behavior and the basic properties of system solution are analyzed and obtained. The basic regeneration number is calculated using the basic regeneration number theorem and analyzes the existence and stability of disease-free equilibrium points and positive equilibrium points. Studies have shown that positive information in the media helps to reduce the spread of infectious diseases.

In this paper, we study the uniqueness and value-sharing of meromorphic functions whose nonlinear differential polynomials share a small function. We remove restrictions and relax the conditions in uniqueness results of the nonlinear differential polynomials, and our results extend the corresponding theorem obtained by Zhang and Thi Hoai An Ta et al..

In this paper, we obtain some criteria for the existence of the periodic solution for the second order nonlinear functional differential equations with delay and variable coefficients$x^{\prime\prime}(t)+p(t)x^{\prime}(t)+q(t)x(t)=\lambda h(t)f(t, x(t-\tau(t))+r(t)x^{\prime}(t)$, by means of fixed point theorem in extend b-metric space.

Time-delay differential equations have important applications in physical chemistry, engineering, information, economy, especially in biological mathematics and many other fields. In this paper, we study the existence of solutions to second-order differential equations with time delays and variation coefficients in a complete b-metric spaces.