Articles

Approximate controllability and complete controllability of semilinear fractional functional differential systems with control

This paper is concerned with the approximate controllability and complete controllability of semilinear fractional functional differential systems with control involving Caputo fractional derivative. By using ...

Authors: Yanhua Wen and Xian-Feng Zhou

Nontrivial solutions for boundary value problems of a fourth order difference equation with sign-changing nonlinearity

In this paper, using the topological degree theory, we establish two existence theorems for nontrivial solutions for boundary value problems of a fourth order difference equation with a sign-changing nonlinear...

Authors: Keyu Zhang, Donal O’Regan and Zhengqing Fu

Strong convergence of the split-step θ-method for stochastic age-dependent capital system with Poisson jumps and fractional Brownian motion

Most stochastic age-dependent capital systems cannot be solved explicitly, so it is necessary to develop numerical methods and study the properties of numerical solutions. In this paper, we consider a class of...

Authors: Ting Kang and Qimin Zhang

Singularity problems to fourth-order Rayleigh equation with time-dependent deviating argument

The paper is devoted to an investigation of the existence of a positive periodic solution for a kind of fourth-order singular Rayleigh equation with time-dependent deviating argument, where the nonlinear term g s...

Authors: Yun Xin and Hongmin Liu

A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay

Allee effect (i.e. sparse effect) is active when the population density is small. Our purpose is to study such an effect of this phenomenon on population dynamics. We investigate an impulsive state feedback co...

Authors: Yaning Li, Huidong Cheng and Yanhui Wang

Coupled Hilfer fractional differential systems with random effects

This paper deals with some existence results for two classes of coupled systems of Hilfer and Hilfer–Hadamard random fractional differential equations. The main tool used to carry out our results is Itoh’s ran...

Authors: Saïd Abbas, Mouffak Benchohra and Yong Zhou

On nonlocal Neumann boundary value problem for a second-order forward \((\alpha,\beta)\)-difference equation

Authors: Thitiporn Linitda and Saowaluck Chasreechai

Portfolio decision with a quadratic utility and inflation risk

This paper considers a portfolio selection problem with a quadratic utility of consumption, which is symmetric with respect to a bliss point. At bliss point, the utility function has its maximum value and furt...

Authors: Byung Hwa Lim and Ho-Seok Lee

Stability analysis of a two-patch predator–prey model with two dispersal delays

This paper deals with a predator–prey model with both species in the delayed-dispersal case in a two-patch environment. The purpose of this paper is to study the effect of two dispersal delays on the stability...

Authors: Guowei Sun and Ali Mai

Solitary and periodic wave solutions of higher-dimensional conformable time-fractional differential equations using the \(( \frac{G'}{G},\frac{1}{G} ) \)-expansion method

Authors: Altaf A. Al-Shawba, Farah A. Abdullah, Khaled A. Gepreel and Amirah Azmi

On the solutions of a max-type system of difference equations with period-two parameters

Authors: Guangwang Su, Taixiang Sun and Bin Qin

Single upper-solution or lower-solution method for Langevin equations with two fractional orders

The purpose of this paper is to investigate the existence and uniqueness of nonnegative solutions for Langevin equations with two fractional orders:

Authors: Chengbo Zhai, Pingping Li and Hongyu Li

High order locally one-dimensional methods for solving two-dimensional parabolic equations

Based on the locally one-dimensional strategy, we propose two high order finite difference schemes for solving two-dimensional linear parabolic equations. In the first method, fourth order approximation in spa...

Authors: Jianhua Chen and Yongbin Ge

Dynamics of a stage-structured single population model with state-dependent delay

In this paper, a novel stage-structured single population model with state-dependent maturity delay is formulated and analyzed. The delay is related to the size of population and taken as a non-decreasing diff...

Authors: Yan Wang, Xianning Liu and Yangjiang Wei

Convergence of neutral type SICNNs involving proportional delays and D operators

In the present study, by employing differential inequality theory, some novel assertions are gained to validate the global exponential convergence on neutral type shunting inhibitory cellular neural networks i...

Authors: Renwei Jia and Shuhua Gong

Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity

Authors: Jing Zhang and Zhongyi Zhang

Solutions induced from bright solitons for nucleon–meson model

Authors: Qihong Shi, Suqin Chang, Xiaobing Zhang and Jianxiong Cao

Correction to: Global and local stability analysis in a nonlinear discrete-time population model

The author would like to apologize for some errors which are published in Ref. [1].

Authors: Özlem Ak Gümüş

Equivalence of the mean square stability between the partially truncated Euler–Maruyama method and stochastic differential equations with super-linear growing coefficients

For stochastic differential equations (SDEs) whose drift and diffusion coefficients can grow super-linearly, the equivalence of the asymptotic mean square stability between the underlying SDEs and the partiall...

Authors: Yanan Jiang, Zequan Huang and Wei Liu

A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel

In this paper, we solve a system of fractional differential equations within a fractional derivative involving the Mittag-Leffler kernel by using the spectral methods. We apply the Chebyshev polynomials as a b...

Authors: D. Baleanu, B. Shiri, H. M. Srivastava and M. Al Qurashi

Semianalytical solutions by homotopy analysis method for EIAV infection with stability analysis

Equine Infectious Anemia Virus (EIAV) is a bovine lentivirus group that creates equine infectious anemia in horses around the globe. In this paper, we propose a basic nonlinear differential equation for EIAV i...

Authors: S. Geethamalini and S. Balamuralitharan

Exponential stability of nonlinear systems with impulsive effects and disturbance input

In this paper, exponential stability of nonlinear systems with impulse time window, disturbance input and bounded gain error is investigated. By means of the above result and the construction of a linear stabi...

Authors: Xingkai Hu and Linru Nie

Numerical algorithms for multidimensional time-fractional wave equation of distributed-order with a nonlinear source term

Fractional differential equations (FDEs) of distributed-order are important in depicting the models where the order of differentiation distributes over a certain range. Numerically solving this kind of FDEs re...

Authors: Jiahui Hu, Jungang Wang and Yufeng Nie

A class of Runge–Kutta methods for nonlinear Volterra integral equations of the second kind with singular kernels

This paper aims to obtain an approximate solution for fractional order Riccati differential equations (FRDEs). FRDEs are equivalent to nonlinear Volterra integral equations of the second kind. In order to solv...

Authors: Bijan Hasani Lichae, Jafar Biazar and Zainab Ayati

Comparative simulations for solutions of fractional Sturm–Liouville problems with non-singular operators

In this study, we consider fractional Sturm–Liouville (S–L) problems within non-singular operators. A fractional S–L problem with exponential and Mittag-Leffler kernels is given with different versions in the ...

Authors: Erdal Bas, Ramazan Ozarslan, Dumitru Baleanu and Ahu Ercan

A Crank–Nicolson linear difference scheme for a BBM equation with a time fractional nonlocal viscous term

In this paper, we construct a Crank–Nicolson linear finite difference scheme for a Benjamin–Bona–Mahony equation with a time fractional nonlocal viscous term. The stability and convergence of the proposed nume...

Authors: Xue Shen and Ailing Zhu

Hopf bifurcation analysis of a delayed SEIR epidemic model with infectious force in latent and infected period

In this paper, we analyze a delayed SEIR epidemic model in which the latent and infected states are infective. The model has a globally asymptotically stable disease-free equilibrium whenever a certain epidemiolo...

Authors: Aekabut Sirijampa, Settapat Chinviriyasit and Wirawan Chinviriyasit

Solution of fractional differential equations via \(\alpha-\psi\)-Geraghty type mappings

Authors: Hojjat Afshari, Sabileh Kalantari and Dumitru Baleanu

Stabilized finite element method for the stationary mixed Stokes–Darcy problem

This paper considers numerical methods for solving the viscous incompressible steady-state Stokes–Darcy problem that can be implemented by the use of existing surface water and groundwater codes. In the porous...

Authors: Jiaping Yu, Md. Abdullah Al Mahbub, Feng Shi and Haibiao Zheng

Oscillation of second order difference equation with several super-linear neutral terms

In this article,we present some new sufficient conditions for the oscillation of all solutions of a second order difference equation with several super-linear neutral terms. The results obtained here extend or...

Authors: S. Mehar Banu and S. Nalini

Iterative learning control for MIMO parabolic partial difference systems with time delay

In this paper, the iterative learning control (ILC) technique is extended to multi-input multi-output (MIMO) systems governed by parabolic partial difference equations with time delay. Two types of ILC algorit...

Authors: Xisheng Dai, Xuemin Tu, Yong Zhao, Guangxing Tan and Xingyu Zhou

Existence results for multi-term fractional differential equations with nonlocal multi-point and multi-strip boundary conditions

In this paper, we discuss the existence and uniqueness of solutions for a new class of multi-point and multi-strip boundary value problems of multi-term fractional differential equations by using standard fixe...

Authors: Ravi P. Agarwal, Ahmed Alsaedi, Najla Alghamdi, Sotiris K. Ntouyas and Bashir Ahmad

Competition and coexistence of a stochastic Holling II n-predator one-prey model

In this paper, we discuss a stochastic Holling II predator–prey model with n-predator competing for one prey. The existence of a positive solution is established by using the comparison theorem. We get the stocha...

Authors: Chunjuan Zhu and Yin Li

Moment closure of infectious diseases model on heterogeneous metapopulation network

The global transmission of infectious diseases poses huge threats to human. Traditional heterogeneous mean-field models on metapopulation networks ignore the heterogeneity of individuals who are in different d...

Authors: Shanshan Feng and Zhen Jin

Dissipativity analysis and stabilization for discontinuous delayed complex-valued networks via matrix measure method

In this paper, we discuss the dissipativity and stabilization problems via matrix measure strategy. First, we propose a way to construct complex-valued set-valued maps and give the basic framework of complex-v...

Authors: Zengyun Wang, Jinde Cao and Zhenyuan Guo

Multiplicity results for a class of fractional differential equations with impulse

In this paper, we apply Morse theory, local linking arguments and the Clark theorem to a study of the multiplicity of nontrivial solutions for a class of impulsive fractional differential equations with Dirich...

Authors: Yulin Zhao, Xiaoyan Shi and Haibo Chen

Global Mittag-Leffler synchronization of delayed fractional-order memristive neural networks

This paper deals with the global Mittag-Leffler synchronization of fractional-order memristive neural networks (FMNNs) with time delay. Since the FMNNs are essentially a class of switched systems with irregula...

Authors: Yingjie Fan, Xia Huang, Zhen Wang, Jianwei Xia and Yuxia Li

Oscillation of second order neutral dynamic equations with deviating arguments on time scales

Authors: Ying Sui and Zhenlai Han

Dynamics of a delayed SEIQ epidemic model

In this work we consider an epidemic model that contains four species susceptible, exposed, infected and quarantined. With this model, first we find a feasible region which is invariant and where the solutions...

Authors: Wanjun Xia, Soumen Kundu and Sarit Maitra

Energy decay rate of multidimensional inhomogeneous Landau–Lifshitz–Gilbert equation and Schrödinger map equation on the sphere

We consider the multidimensional dimensional inhomogeneous Landau–Lifshitz–Gilbert (ILLG) equation and its degenerate case, the Schrödinger map equation. We investigate the special solutions (under large initi...

Authors: Penghong Zhong, Chao Zhang and Fengong Wu

Dispersive analytical soliton solutions of some nonlinear waves dynamical models via modified mathematical methods

We have employed a modified form of the F-expansion technique on four nonlinear waves models and obtained numerous exact and soliton wave solutions in a different form. New constructed solutions showed the sig...

Authors: Asghar Ali, Aly R. Seadawy and Dianchen Lu

Exact controllability of fractional order evolution equations in Banach spaces

In this paper, we deal with the exact controllability of a class of fractional evolution equations with time-varying delay. Under the nonlocal condition, the exact controllability of this system is established...

Authors: Yi Cheng, Shanshan Gao and Yuhu Wu

Periodic solutions to a coupled two-dimensional lattice presented by Blaszak and Szum with Riemann–theta function

A coupled two-dimensional lattice presented by Blaszak and Szum is studied with the aid of Riemann–theta function and the bilinear method. By utilizing a bilinear form of the equation, we have obtained one-per...

Authors: Ting Su

Two numerical methods for fractional partial differential equation with nonlocal boundary value problem

The exact solution of fractional telegraph partial differential equation of nonlocal boundary value problem is obtained. The theorem of stability estimates is presented for this equation. Difference schemes ar...

Authors: Mahmut Modanlı

Bifurcation analysis in a diffusive predator–prey system with Michaelis–Menten-type predator harvesting

In this paper, we consider a modified predator–prey model with Michaelis–Menten-type predator harvesting and diffusion term. We give sufficient conditions to ensure that the coexisting equilibrium is asymptoti...

Authors: Qiannan Song, Ruizhi Yang, Chunrui Zhang and Leiyu Tang

Outer synchronization of a class of mixed delayed complex networks based on pinning control

In this paper, the problem on outer synchronization is investigated for a class of mixed delayed complex networks by using the pinning control strategy. Together with some Lyapunov–Krasovskii functional and ef...

Authors: Lin Shi, Guiling Chen and Shouming Zhong

Implicit coupled Hilfer–Hadamard fractional differential systems under weak topologies

In this article, we present some existence of weak solutions for a coupled system of implicit fractional differential equations of Hilfer–Hadamard type. Our approach is based on Mönch’s fixed point theorem ass...

Authors: Saïd Abbas, Mouffak Benchohra, Naima Hamidi and Yong Zhou

Conservation laws, symmetry reductions, and exact solutions of some Keller–Segel models

In this paper, three Keller–Segel models are considered from the point of Lie symmetry analysis, conservation laws, symmetry reduction, and exact solutions. By means of Lie symmetry analysis, we first obtain a...

Authors: Lihua Zhang and Fengsheng Xu

Homoclinic solutions for Hamiltonian system with impulsive effects

In this article, we investigate a class of impulsive Hamiltonian systems with a p-Laplacian operator. By establishing a series of new sufficient conditions, the existence of homoclinic solutions to such type of s...

Authors: Jian Liu, Lizhao Yan, Fei Xu and Mingyong Lai

Stability analysis of a fractional-order predator–prey model incorporating a constant prey refuge and feedback control

In this paper, a kind of fractional-order predator–prey (FOPP) model with a constant prey refuge and feedback control is considered. By analyzing characteristic equations, we carry out detailed discussion with...

Authors: Hong-Li Li, Ahmadjan Muhammadhaji, Long Zhang and Zhidong Teng