Articles

Stability analysis of discrete-time multi-patch Beddington–DeAngelis type predator-prey model with time-varying delay

This paper is concerned with the stability of a discrete-time multi-patch Beddington–DeAngelis type predator-prey model with time-varying delay, where the dispersal of both predators and prey is considered. A ...

Authors: Jiqiang Feng and Zhiqiang Zhao

Solitons for the modified \((2 + 1)\)-dimensional Konopelchenko–Dubrovsky equations

Authors: Xiumei Lyu and Wei Gu

Hopf bifurcation of a delayed worm model with two latent periods

We investigate a delayed epidemic model for the propagation of worm in wireless sensor network with two latent periods. We derive sufficient conditions for local stability of the worm-induced equilibrium of th...

Authors: Juan Liu and Zizhen Zhang

Existence and stability results for multi-time scale stochastic fractional neural networks

We apply the tools of functional analysis to investigate the existence and uniqueness of solutions for multi-scale stochastic fractional neutral networks. By constructing a descent Lyapunov functional, the asy...

Authors: Dehua Wang, Xiao-Li Ding and Bashir Ahmad

Entire solutions for a delayed lattice competitive system

In this paper, we investigate the existence of entire solutions for a delayed lattice competitive system. Here the entire solutions are the solutions that exist for all ...

Authors: Rui Yan, Yang Wang and Meiping Yao

On applications of Caputo k-fractional derivatives

This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et a...

Authors: Ghulam Farid, Naveed Latif, Matloob Anwar, Ali Imran, Muhammad Ozair and Madeeha Nawaz

A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area

For the boundary value problem (BVP) of a second-order partial differential equation on a plane triangle area, we propose a new algorithm based on the Adomian decomposition method (ADM) combined with a segment...

Authors: Yin-shan Yun, Ying Wen, Temuer Chaolu and Randolph Rach

Further results on the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays

In this paper, the investigation of the asymptotic stability of Riemann–Liouville fractional neutral systems with variable delays has been presented. The advantage of the Lyapunov functional was used to achiev...

Authors: Yener Altun

Stability analysis of a nonlinear coupled implicit switched singular fractional differential system with p-Laplacian

This paper deals with existence, uniqueness, and Hyers–Ulam stability of solutions to a nonlinear coupled implicit switched singular fractional differential system involving Laplace operator ...

Authors: Manzoor Ahmad, Akbar Zada and Jehad Alzabut

Some symmetries, similarity solutions and various conservation laws of a type of dispersive water waves

We investigate the point symmetries, Lie–Bäcklund symmetries for a type of dispersive water waves. We obtain some Lie transformation groups, various group-invariant solutions, and some similarity solutions. Be...

Authors: Yufeng Zhang, Na Bai and Hongyang Guan

Numerical treatment of stochastic heroin epidemic model

We have presented the numerical analysis of a stochastic heroin epidemic model in this paper. The mean of stochastic heroin model is itself a deterministic solution. The effect of reproduction number has also ...

Authors: M. Rafiq, Ali Raza, M. Usman Iqbal, Zubair Butt, Hafiza Anum Naseem, M. Ali Akram, M. Kamran Butt, Adil Khaliq, Qurat-ul-Ain and Shamrash Azam

Stationary distribution of a stochastic SIRD epidemic model of Ebola with double saturated incidence rates and vaccination

In this paper, a stochastic SIRD model of Ebola with double saturated incidence rates and vaccination is considered. Firstly, the existence and uniqueness of a global positive solution are obtained. Secondly, ...

Authors: Panpan Wang and Jianwen Jia

Modeling the spread of porcine reproductive and respiratory syndrome virus (PRRSV) in a swine population: transmission dynamics, immunity information, and optimal control strategies

Porcine reproductive and respiratory syndrome (PRRS) is an important swine disease that affects many swine industries worldwide. The disease can cause reproductive failure and respiratory problems in a swine p...

Authors: Phithakdet Phoo-ngurn, Chanakarn Kiataramkul and Farida Chamchod

Some representations of the general solution to a difference equation of additive type

Authors: Stevo Stević

Levinson type inequalities for higher order convex functions via Abel–Gontscharoff interpolation

In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel–Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for t...

Authors: Muhammad Adeel, Khuram Ali Khan, Ðilda Pečarić and Josip Pečarić

The Euler scheme for stochastic differential equations with discontinuous drift coefficient: a numerical study of the convergence rate

The Euler scheme is one of the standard schemes to obtain numerical approximations of solutions of stochastic differential equations (SDEs). Its convergence properties are well known in the case of globally Li...

Authors: S. Göttlich, K. Lux and A. Neuenkirch

An analytical approach to obtain exact solutions of some space-time conformable fractional differential equations

In this paper, the sine-Gordon expansion method is used to obtain analytical solutions of the conformable space-time generalized reaction Duffing model and conformable space-time Eckhaus equation with the aid ...

Authors: Nematollah Kadkhoda and Hossein Jafari

Some new inequalities for generalized fractional conformable integral operators

Authors: Kottakkaran Sooppy Nisar, Gauhar Rahman and Aftab Khan

Oscillation of third-order neutral differential equations with damping and distributed delay

The present paper focuses on the oscillation of the third-order nonlinear neutral differential equations with damping and distributed delay. The oscillation of the third-order damped equations is often discuss...

Authors: Meihua Wei, Cuimei Jiang and Tongxing Li

New parameterized quantum integral inequalities via η-quasiconvexity

Authors: Eze R. Nwaeze and Ana M. Tameru

Some Tauberian conditions on logarithmic density

This article is based on the study on the λ-statistical convergence with respect to the logarithmic density and de la Vallee Poussin mean and generalizes some results of logarithmic λ-statistical convergence and ...

Authors: Adem Kılıçman, Stuti Borgohain and Mehmet Küçükaslan

Existence and multiplicity results for some generalized Hammerstein equations with a parameter

Authors: Lucía López-Somoza and Feliz Minhós

On single-step HSS iterative method with circulant preconditioner for fractional diffusion equations

By exploiting Toeplitz-like structure and non-Hermitian dense property of the discrete coefficient matrix, a new double-layer iterative method called SHSS-PCG method is employed to solve the linear systems ori...

Authors: Mu-Zheng Zhu, Guo-Feng Zhang and Ya-E Qi

Applying new fixed point theorems on fractional and ordinary differential equations

In this paper, we consider a fixed point theorem that extends and unifies several existing results in the literature. We apply the proven fixed point results on the existence of solution of ordinary boundary v...

Authors: Erdal Karapınar, Thabet Abdeljawad and Fahd Jarad

Persistence of global well-posedness for the 2D Boussinesq equations with fractional dissipation

In this paper, we study the IBVP for the 2D Boussinesq equations with fractional dissipation in the subcritical case, and prove the persistence of global well-posedness of strong solutions. Moreover, we also p...

Authors: Xing Su, Gangwei Wang and Yue Wang

Green’s function homotopy perturbation method for the initial-boundary value problems

This article deals with the novel method for finding solutions for the initial-boundary value problems (IBVPs), which is called the Sawangtong’s Green function homotopy perturbation method, shortly called SGHP...

Authors: Wannika Sawangtong and Panumart Sawangtong

Analysis of two Legendre spectral approximations for the variable-coefficient fractional diffusion-wave equation

In this paper, we solve the variable-coefficient fractional diffusion-wave equation in a bounded domain by the Legendre spectral method. The time fractional derivative is in the Caputo sense of order

Authors: Wenping Chen, Shujuan Lü, Hu Chen and Lihua Jiang

A new parallel difference algorithm based on improved alternating segment Crank–Nicolson scheme for time fractional reaction–diffusion equation

The fractional reaction–diffusion equation has profound physical and engineering background, and its rapid solution research is of important scientific significance and engineering application value. In this p...

Authors: Xiaozhong Yang and Xu Dang

Random attractors for the stochastic coupled suspension bridge equations of Kirchhoff type

This paper is devoted to the dynamical behavior of stochastic coupled suspension bridge equations of Kirchhoff type. For the deterministic cases, there are many classical results such as existence and uniquene...

Authors: Ling Xu, Jianhua Huang and Qiaozhen Ma

Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator

This paper is concerned with an integral boundary value problem of fractional differential equations with p-Laplacian operator. Sufficient conditions ensuring the existence of extremal solutions for the given pro...

Authors: Ying He and Bo Bi

A delayed e-epidemic SLBS model for computer virus

Authors: Zizhen Zhang, Sangeeta Kumari and Ranjit Kumar Upadhyay

Numerical solutions of nonlinear fractional model arising in the appearance of the strip patterns in two-dimensional systems

The main aim of this paper is to present a comparative study of modified analytical technique based on auxiliary parameters and residual power series method (RPSM) for Newell–Whitehead–Segel (NWS) equations of...

Authors: Sunil Kumar, Amit Kumar, Shaher Momani, Mujahed Aldhaifallah and Kottakkaran Sooppy Nisar

Chaos, control, and synchronization in some fractional-order difference equations

In this paper, we propose three fractional chaotic maps based on the well known 3D Stefanski, Rössler, and Wang maps. The dynamics of the proposed fractional maps are investigated experimentally by means of ph...

Authors: Amina-Aicha Khennaoui, Adel Ouannas, Samir Bendoukha, Giuseppe Grassi, Xiong Wang, Viet-Thanh Pham and Fawaz E. Alsaadi

Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations

Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The unique...

Authors: Bingxian Wang, Bin Yang and Mei Xu

Determinants and inverses of perturbed periodic tridiagonal Toeplitz matrices

In this paper, we deal mainly with a class of periodic tridiagonal Toeplitz matrices with perturbed corners. By matrix decomposition with the Sherman–Morrison–Woodbury formula and constructing the correspondin...

Authors: Yunlan Wei, Xiaoyu Jiang, Zhaolin Jiang and Sugoog Shon

Host-pathogen interaction for larvae oysters with salinity dependent transmission

Mathematical models of host-pathogen interactions are proposed and analyzed. Here hosts are oyster population in a free-swimming larval stage and assumably live in the closed homogeneous environment. In terms ...

Authors: Kalanyu Sunthawanic, Kornkanok Bunwong and Wichuta Sae-jie

Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under...

Authors: Aliyu Isa Aliyu, Ali Saleh Alshomrani, Yongjin Li, Mustafa Inc and Dumitru Baleanu

Stability of discrete-time HIV dynamics models with three categories of infected CD4⁺ T-cells

This paper studies the global stability of two discrete-time HIV infection models. The models integrate (i) latently infected cells, (ii) long-lived chronically infected cells and (iii) short-lived infected ce...

Authors: A. M. Elaiw and M. A. Alshaikh

Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion

In the literature, many generalizations of continued fractions have been introduced, and for each of them, convergence results have been proved. In this paper, we suggest a definition of generalized continued ...

Authors: Hendrik Baumann

Fractional order ecological system for complexities of interacting species with harvesting threshold in imprecise environment

The key objective of this paper is to study the imprecise biological complexities in the interaction of two species pertaining to harvesting threshold. It is explained by taking the prey–predator model with im...

Authors: Najeeb Alam Khan, Oyoon Abdul Razzaq, Sankar Parsad Mondal and Qammar Rubbab

Oscillation and nonoscillation theorems of neutral dynamic equations on time scales

Authors: Yong Zhou, Ahmed Alsaedi and Bashir Ahmad

Endpoint regularity of discrete multilinear fractional nontangential maximal functions

Authors: Daiqing Zhang

Study of nonlinear Pachpatte’s inequalities on time scales

In this paper, we develop a fundamental dynamic inequality, a generalization of comparison theorem and reproduce the proofs of some nonlinear integral Pachpatte’s inequalities by using their continuous analogu...

Authors: Sarah Sarfaraz, Naveed Ahmad and Ghaus ur Rahman

Non-linear population discrete models with two time scales: re-scaling of part of the slow process

In this work we present a reduction result for discrete-time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in prac...

Authors: Luis Sanz, Rafael Bravo de la Parra, Marcos Marvá and Eva Sánchez

A stabilized coupled method and its optimal error estimates for elliptic interface problems

In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provi...

Authors: Jiaping Yu, Feng Shi and Jianping Zhao

Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure

Diffusion-driven instability is a basic nonlinear mechanism for pattern formation. Therefore, the way of population diffusion may play a determinative role in the spatiotemporal dynamics of biological systems....

Authors: Tousheng Huang, Huayong Zhang, Zhengran Hu, Ge Pan, Shengnan Ma, Xiumin Zhang and Zichun Gao

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

We show that the Stirling numbers of the first and second kind can be represented in terms of moments of appropriate random variables. This allows us to obtain, in a unified way, a variety of old and new expli...

Authors: José A. Adell and Alberto Lekuona

Neimark–Sacker bifurcation of a chemotherapy treatment of glioblastoma multiform (GBM)

In this paper, we propose a system of differential equations with piecewise constant arguments to describe the growth of GBM under chemotherapeutic treatment and the interaction among the glial cells, the canc...

Authors: F. Bozkurt and A. Yousef

Numerical solution of stochastic state-dependent delay differential equations: convergence and stability

Numerical analysis of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple feature. In this paper, we aim to study a more general cas...

Authors: Bahar Akhtari

A non-autonomous impulsive food-chain model with delays

A non-autonomous almost periodic prey–predator system with impulsive effects and multiple delays is proposed in this paper, Holling’s type-IV systems and ratio-dependent functional responses are also involved ...

Authors: Baodan Tian, Pengkai Zhang, Jiamei Li, Yong Zhang and Liu Yang