This paper is concerned with a class of triple-point integral boundary value problems for impulsive fractional differential equations involving the Riemann-Liouville fractional derivative of order α ( 2 < α ≤ 3 ). Some sufficient criteria for the existence of solutions are obtained by applying the contraction mapping principle and the fixed point theorem. As an application, one...

By utilizing the coincidence degree theory and the related continuation theorem, as well as some prior estimates, we investigate the existence of positive periodic solutions of a neutral predator-prey system with monotone functional responses. New sufficient criteria are established for the existence of periodic solutions. Some well-known results in the literature are generalized...

In this paper, we study the existence and multiplicity of solutions for an impulsive differential equation via some critical point theory and the variational method. We extend and improve some recent results and reduce conditions.

In this paper, we study the existence of nontrivial homoclinic orbits of a dynamic equation on time scales T of the form { ( p ( t ) u Δ ( t ) ) Δ + q σ ( t ) u σ ( t ) = f ( σ ( t ) , u σ ( t ) ) , △ -a.e. t ∈ T , u ( ± ∞ ) = u Δ ( ± ∞ ) = 0 . We construct a variational framework of the above-mentioned problem, and some new results on the existence of a homoclinic orbit or an...

In this paper we consider the existence of nonoscillatory solutions for a system of higher-order neutral differential equations with distributed coefficients and delays. We use the B a n a c h contraction principle to obtain new sufficient conditions for the existence of nonoscillatory solutions.

This paper considers two kinds of novel decoupled algorithms for the non-stationary Stokes-Darcy model. In this way, the considered problem is decoupled into one time-dependent Stokes equations and one linear parabolic equation. For the two algorithms, we establish the stability and the optimal error estimates. Furthermore, the existing result in Mu and Zhu (Math. Comput. 79:707...

The main purpose of this paper is, using the method of trigonometric sums and the properties of Gauss sums, to study the computational problem of one kind of congruence equation modulo an odd prime and give some interesting fourth-order linear recurrence formulas. MSC: 11L05.

This study investigates the problem of finite-time control for uncertain systems with nonlinear perturbations. The aim is to design the state-feedback and output-feedback controller which ensure finite-time boundedness and with a desired H ∞ performance index υ. Specifically, first, we divide the time-varying delay into non-uniformly subintervals and decompose the corresponding...

This paper is concerned with a diffusive and delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary conditions. Preliminary analyses on the well-posedness of solutions and the dissipativeness of the system are presented with assistance of inequality technique. Then the Hopf bifurcation induced by spatial...

In this paper, relying on Nevanlinna theory of the value distribution of meromorphic functions, we mainly study meromorphic solutions of certain types of q-difference differential equations, obtain estimates of the growth order of their meromorphic solutions, and give a number of examples to show what our results are the best possible in certain senses. Improvements and...

This paper investigates the absolute stability problem of time-varying delay Lurie indirect control systems with variable coefficients. A positive-definite Lyapunov-Krasovskii functional is constructed. Some novel sufficient conditions for absolute stability of Lurie systems with single nonlinearity are obtained by estimating the negative upper bound on its total time derivative...

We apply an iterative reproducing kernel Hilbert space method to get the solutions of fractional Riccati differential equations. The analysis implemented in this work forms a crucial step in the process of development of fractional calculus. The fractional derivative is described in the Caputo sense. Outcomes are demonstrated graphically and in tabulated forms to see the power of...

This paper is concerned with the existence of positive solutions for integral boundary value problems of Caputo fractional differential equations with p-Laplacian operator. By means of the properties of the Green’s function, Avery-Peterson fixed point theorems, we establish conditions ensuring the existence of positive solutions for the problem. As an application, an example is...

In this paper, we apply a new method, a delayed matrix exponential, to study P-type and D-type learning laws for time-delay controlled systems to track the varying reference accurately by using a few iterations in a finite time interval. We present open-loop P- and D-type asymptotic convergence results in the sense of λ-norm by virtue of spectral radius of matrix. Finally, four...

This paper is concerned with the problem of a passivity analysis for a class of memristor-based neural networks with multiple proportional delays and the state estimator is designed for the memristive system through the available output measurements. By constructing a proper Lyapunov-Krasovskii functional, new criteria are obtained for the passivity and state estimation of the...

In this paper, an age-structured epidemiological process is considered. The disease model is based on a SIR model with unknown parameters. We addressed two important issues to analyzing the model and its parameters. One issue is concerned with the theoretical existence of unique solution, the identifiability problem. The second issue is how to estimate the parameters in the model...

We generalize a delayed computer virus model, known as the SLBQRS model in a computer network, by introducing the time delay due to the period that the antivirus software uses to clean viruses in the breaking out computers and the quarantined computers. By choosing the delay as the parameter, we prove the existence of a Hopf bifurcation as the delay crosses a critical value...

The purpose of this paper is to study oscillation of Runge-Kutta methods for linear advanced impulsive differential equations with piecewise constant arguments. We obtain conditions of oscillation and nonoscillation for Runge-Kutta methods. Moreover, we prove that the oscillation of the exact solution is preserved by the θ-methods. It turns out that the zeros of the piecewise...

The objective of this paper is to explore the long time behavior of a stochastic SIR model. We establish a threshold condition called the basic reproduction number under stochastic perturbation for persistence or extinction of the disease. Especially, some numerical simulations are applied to support our theoretical results. MSC: 49K15, 60H10, 93E15.

Dolgy et al. introduced the modified degenerate Bernoulli polynomials, which are different from Carlitz’s degenerate Bernoulli polynomials (see Dolgy et al. in Adv. Stud. Contemp. Math. (Kyungshang) 26(1):1-9, 2016 ). In this paper, we study some explicit identities and properties for the modified degenerate q-Bernoulli polynomials arising from the p-adic invariant integral on Z...

In this work, we study Hopf bifurcations in the extended Lorenz system, x ˙ = y , y ˙ = m x − n y − m x z − p x 3 , z ˙ = − a z + b x 2 , with five parameters m , n , p , a , b ∈ R . For some values of the parameters, this system can be transformed to the classical Lorenz system. In this paper, we give conditions for occurrence of Hopf bifurcation at the equilibrium points. We...

In this paper, a new implementation of the reproducing kernel method is proposed in order to obtain the accurate numerical solution of two-point boundary value problems with Dirichlet boundary conditions. Based on reproducing kernel theory, reproducing kernel functions with polynomial form will be constructed in the reproducing kernel spaces spanned by the Chebyshev basis...

The concern of the paper is nonconstant positive solutions of a class of Lotka-Volterra competition systems over 1D domains. We prove the existence of a positive monotonous solution to the shadow system for each small diffusion rate ϵ > 0 . Our theoretical results provide a foundation for further theoretical analysis on the shadow system and give insights on how diffusion and...

In this paper, a wavelet numerical method for solving nonlinear Volterra integro-differential equations of fractional order is presented. The method is based upon Euler wavelet approximations. The Euler wavelet is first presented and an operational matrix of fractional-order integration is derived. By using the operational matrix, the nonlinear fractional integro-differential...

We discuss the existence and uniqueness of a solution of a boundary value problem for a class of nonlinear fractional functional differential equations with delay involving Caputo fractional derivative. Our work relies on the Schauder fixed point theorem and contraction mapping principle in a cone. We also include examples to show the applicability of our results. MSC: 34K37, 34B15.