Articles

New results of exponential synchronization of complex network with time-varying delays

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...

Authors: Yiping Luo, Zhaoming Ling, Zifeng Cheng and Bifeng Zhou

Logical entropy of dynamical systems in product MV-algebras and general scheme

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...

Authors: Dagmar Markechová and Beloslav Riečan

Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions

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...

Authors: Asma, Arshad Ali, Kamal Shah and Fahd Jarad

Backward bifurcation of predator–prey model with anti-predator behaviors

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 ...

Authors: Guangyao Tang and Wenjie Qin

Dissipativity analysis of neutral-type memristive neural network with two additive time-varying and leakage delays

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...

Authors: Cuiping Yang, Zuoliang Xiong and Tianqing Yang

Ulam stability results to a class of nonlinear implicit boundary value problems of impulsive fractional differential equations

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...

Authors: A. Ali, K. Shah and D. Baleanu

On almost periodicity of solutions of second-order differential equations involving reflection of the argument

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...

Authors: Peiguang Wang, Dhaou Lassoued, Syed Abbas, Akbar Zada and Tongxing Li

Multiple periodic solutions of high order differential delay equations with \(2k-1\) lags

Authors: Lin Li, Huafei Sun and Weigao Ge

Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent

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 ...

Authors: Zhenzhen Shi, Jianmei Wang, Qingjian Li and Huidong Cheng

An optimized Crank–Nicolson finite difference extrapolating model for the fractional-order parabolic-type sine-Gordon equation

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...

Authors: Yanjie Zhou and Zhendong Luo

Master–slave synchronization of a class of fractional-order Takagi–Sugeno fuzzy neural networks

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,...

Authors: Bei Zhang, Jinsen Zhuang, Haidong Liu, Jinde Cao and Yonghui Xia

Application of reproducing kernel Hilbert space method for solving second-order fuzzy Volterra integro-differential equations

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 ...

Authors: Ghaleb N. Gumah, Mohammad F. M. Naser, Mohammed Al-Smadi and Shrideh K. Al-Omari

Exponential time differencing schemes for the 3-coupled nonlinear fractional Schrödinger equation

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...

Authors: Xiao Liang and Harish Bhatt

Representations of solutions to linear and bilinear difference equations and systems of bilinear difference equations

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...

Authors: Stevo Stević

New oscillation theorems for second order quasi-linear difference equations with sub-linear neutral term

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the second order neutral difference equation

Authors: M. Nazreen Banu and S. Mehar Banu

Singularities of attractive and repulsive type for p-Laplacian generalized Liénard 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...

Authors: Yun Xin and Hongmin Liu

A novel improved extreme learning machine algorithm in solving ordinary differential equations by Legendre neural network methods

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...

Authors: Yunlei Yang, Muzhou Hou and Jianshu Luo

On fractional derivatives with generalized Mittag-Leffler kernels

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...

Authors: Thabet Abdeljawad and Dumitru Baleanu

Fujita-type theorems for a class of coupled semilinear parabolic systems with gradient terms

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...

Authors: Guanming Gai, Qiang Liu, Yang Na and Mingjun Zhou

Positive solutions for a system of second-order discrete boundary value problems

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...

Authors: Ravi P. Agarwal and Rodica Luca

A method for fractional Volterra integro-differential equations by Laguerre polynomials

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...

Authors: Dilek Varol Bayram and Ayşegül Daşcıoğlu

Pricing vulnerable options with variable default boundary under jump-diffusion processes

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...

Authors: Qing Zhou, Qian Wang and Weixing Wu

A class of implicit symmetric symplectic and exponentially fitted Runge–Kutta–Nyström methods for solving oscillatory problems

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...

Authors: Huai Yuan Zhai, Wen Juan Zhai and Bing Zhen Chen

Error estimates of a semi-discrete LDG method for the system of damped acoustic wave equation

Authors: Dojin Kim

Stabilized lowest equal-order mixed finite element method for the Oseen viscoelastic fluid flow

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...

Authors: Shahid Hussain, Md. Abdullah Al Mahbub, Nasrin Jahan Nasu and Haibiao Zheng

Global threshold dynamics of a stochastic epidemic model incorporating media coverage

In this paper, we investigate the global threshold dynamics of a stochastic SIS epidemic model incorporating media coverage. We give the basic reproduction number ...

Authors: Bin Yang, Yongli Cai, Kai Wang and Weiming Wang

Non-smooth analysis method in optimal investment-BSDE approach

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...

Authors: Helin Wu, Yong Ren and Feng Hu

New exact solutions of fractional Cahn–Allen equation and fractional DSW system

This work explores the new exact solutions of nonlinear fractional partial differential equations (FPDEs). The solutions are obtained by adopting an effective technique, the first integral method (FIM). The Ri...

Authors: Shumaila Javeed, Summaya Saif and Dumitru Baleanu

Normal curves in n-dimensional Euclidean space

In this paper, we give a generalization of normal curves to n-dimensional Euclidean space. Then we obtain a necessary and sufficient condition for a curve to be a normal curve in the n-dimensional Euclidean space...

Authors: Özcan Bektaş

Existence and Hyers–Ulam stability for three-point boundary value problems with Riemann–Liouville fractional derivatives and integrals

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...

Authors: Lei Xu, Qixiang Dong and Gang Li

Dynamical analysis in explicit continuous iteration algorithm and its applications

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...

Authors: Qingyi Zhan, Zhifang Zhang and Xiangdong Xie

Threshold dynamics of a delayed predator–prey model with impulse via the basic reproduction number

In this paper, we study a delayed predator–prey model with impulse and, in particular, the existence of the predator-free periodic solution. We employ the approach and techniques coming from epidemiology and c...

Authors: Xiangsen Liu and Binxiang Dai

Existence of solutions for a multi-point boundary value problem with a \(p(r)\)-Laplacian

Authors: Zhiguo Luo and Jinfang Liang

Hyers–Ulam stability and existence criteria for coupled fractional differential equations involving p-Laplacian operator

In this article, by using nonlinear Leray–Schauder-type alternative and Banach’s fixed point theorem, we investigate existence and uniqueness of solutions. We also prove Hyers–Ulam stability for the proposed c...

Authors: Hasib Khan, Wen Chen, Aziz Khan, Tahir S. Khan and Qasem M. Al-Madlal

Predicting the effectiveness of drug interventions with ‘HIV counseling & testing’ (HCT) on the spread of HIV/AIDS: a theoretical study

In this paper, a dynamic compartmental model is constructed for the transmission of HIV/AIDS receiving drug treatment and knowledge from effective awareness programs through media. Using stability theory of di...

Authors: Priti Kumar Roy and Shubhankar Saha

New aspects of Opial-type integral inequalities

In this manuscript, we prove new aspects for several Opial-type integral inequalities for the left and right Caputo–Fabrizio operators with nonsingular kernel. For this purpose we use the inequalities obtained...

Authors: Yasemin Başcı and Dumitru Baleanu

Approximation by quaternion \((p,q)\)-Bernstein polynomials and Voronovskaja type result on compact disk

Authors: Haifa Bin Jebreen, Mohammad Mursaleen and Ambreen Naaz

Parameter uniform numerical method for a system of two coupled singularly perturbed parabolic convection-diffusion equations

In this paper, we propose a numerical scheme for a system of two linear singularly perturbed parabolic convection-diffusion equations. The presented numerical scheme consists of a classical backward-Euler sche...

Authors: Li-Bin Liu, Guangqing Long and Yong Zhang

Existence of periodic solutions for a higher-order neutral difference equation

Based on a continuation theorem of Mawhin, the existence of a periodic solution for a higher-order nonlinear neutral difference equation is studied. Our conclusion is new and interesting.

Authors: Jiao-Ling Zhang and Gen-Qiang Wang

Dynamics of difference equation \(x_{n+1}=f( x_{n-l},x_{n-k})\)

In this paper, we present the asymptotic behavior of the solutions for a general class of difference equations. We introduce general theorems in order to study the stability and periodicity of the solutions. M...

Authors: Osama Moaaz

Oscillatory behavior of solutions of certain fractional difference equations

Authors: Hakan Adiguzel

Homoclinic solutions for n-dimensional p-Laplacian neutral differential systems with a time-varying delay

Authors: Fang Gao and Wenbin Chen

Global behavior of positive solutions for some semipositone fourth-order problems

Authors: Dongliang Yan and Ruyun Ma

Weak convergence of the complex fractional Brownian motion

In this paper, we obtain two approximations in law of the complex fractional Brownian motion by processes constructed from a Poisson process and a Lévy process, respectively.

Authors: Liheng Sang, Guangjun Shen and Qingbo Wang

Finite difference scheme for simulating a generalized two-dimensional multi-term time fractional non-Newtonian fluid model

A finite difference scheme, based upon the Crank–Nicolson scheme, is applied to the numerical approximation of a two-dimensional time fractional non-Newtonian fluid model. This model not only possesses a multi...

Authors: Yanqin Liu, Xiuling Yin, Libo Feng and Hongguang Sun

Permanence and extinction of a high-dimensional stochastic resource competition model with noise

In this paper, we investigate the asymptotic behavior for a kind of resource competition model with environmental noises. Considering the impact of white noise on birth rate and death rate separately, we first...

Authors: Li Wang, Xiaoqiang Wang and Qimin Zhang

Weak θ-contractions and some fixed point results with applications to fractal theory

In this paper, we define weak θ-contractions on a metric space into itself by extending θ-contractions introduced by Jleli and Samet (J. Inequal. Appl. 2014:38, 2014) and utilize the same to prove some fixed poin...

Authors: Mohammad Imdad, Waleed M. Alfaqih and Idrees A. Khan

Stabilization for two-dimensional delta operator systems with time-varying delays and actuator saturation

In this paper, stabilization is studied for a two-dimensional delta operator system with time-varying delays and actuator saturation. Both lower and upper bounds of the time-varying delays are considered. An e...

Authors: Dan Peng, Ting Zhang and Hongjiu Yang

Hopf-zero bifurcation of Oregonator oscillator with delay

In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by per...

Authors: Yuting Cai, Liqin Liu and Chunrui Zhang

Fast convergent average consensus of multiagent systems based on community detection algorithm

In this paper, we consider fast convergent average consensus based on community detection algorithm. Generally, we know that a small network can have a faster convergence speed than a big one at the same condi...

Authors: Xinlei Feng and Xiaoli Yang