The theory of difference equations, the methods used, and their wide applications have advanced beyond their adolescent stage to occupy a central position in applicable analysis. In fact, in the last 15 years, the proliferation of the subject has been witnessed by hundreds of research articles, several monographs, many international conferences, and numerous special sessions.The theory of differential and difference equations forms two extreme representations of real world problems. For example, a simple population model when represented as a differential equation shows the good behavior of solutions whereas the corresponding discrete analogue shows the chaotic behavior. The actual behavior of the population is somewhere in between.The aim of Advances in Difference Equations is to report mainly the new developments in the field of difference equations, and their applications in all fields. We will also consider research articles emphasizing the qualitative behavior of solutions of ordinary, partial, delay, fractional, abstract, stochastic, fuzzy, and set-valued differential equations.Advances in Difference Equations will accept high-quality articles containing original research results and survey articles of exceptional merit.
差分方程的理论、所使用的方法及其广泛的应用已经超越了它们的青少年阶段，在应用分析中占据了中心地位。事实上，在过去的15年里，这一主题的扩散已经见证了数百篇研究文章，几本专著，许多国际会议和无数的特别会议。微分和差分方程理论形成了现实世界问题的两种极端表现形式。例如，一个简单的种群模型在表示为微分方程时表现出解的良好行为，而相应的离散模拟则表现出混沌行为。人口的实际行为介于两者之间。差分方程进展的目的主要是报告差分方程领域的新发展，及其在所有领域的应用。我们也会考虑强调常微分方程、偏微分方程、时滞微分方程、分数阶微分方程、抽象微分方程、随机微分方程、模糊微分方程和集值微分方程的定性行为的研究论文。差分方程进展将接受包含原创研究成果的高质量论文和具有特殊价值的综述性论文。
Two computational approaches for solving a fractional obstacle system in Hilbert space
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-1996-5
Dynamics of a stochastic SIS epidemic model with nonlinear incidence rates
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-1980-0
The fractional form of a new three-dimensional generalized Hénon map
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2064-X
Ulam–Hyers stability analysis to a class of nonlinear implicit impulsive fractional differential equations with three point boundary conditions
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-018-1943-X
Fractional hybrid differential equations with three-point boundary hybrid conditions
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2067-7
Chaos, control, and synchronization in some fractional-order difference equations
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2343-6
Robust adaptive synchronization of complex network with bounded disturbances
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2374-z
Dissipative criteria for Takagi–Sugeno fuzzy Markovian jumping neural networks with impulsive perturbations using delay partitioning approach
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2085-5
Two modified least-squares iterative algorithms for the Lyapunov matrix equations
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2253-7
Optical soliton solutions to the (2+1)$(2+1)$-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2377-9
Bifurcation, chaos analysis and control in a discrete-time predator–prey system
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-1950-6
Modeling the spread of porcine reproductive and respiratory syndrome virus (PRRSV) in a swine population: transmission dynamics, immunity information, and optimal control strategies
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2351-6
Multiple positive solutions for nonlinear mixed fractional differential equation with p-Laplacian operator
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2041-4
Solvability of a general class of two-dimensional hyperbolic-cotangent-type systems of difference equations
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2233-Y
Weighted dynamic inequalities of Opial-type on time scales
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2325-8
One dimensional fractional frequency Fourier transform by inverse difference operator
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2071-Y
Existence of traveling wave solutions with critical speed in a delayed diffusive epidemic model
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2432-6
Adaptive tracking control for a class of uncertain switched stochastic nonlinear systems
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-1975-X
Effects of the wind speeds on heat transfer in a street canyon with a skytrain station
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2175-4
Multiple bifurcations and periodic coexistence in a delayed Hopfield two-neural system with a monotonic activation function
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2066-8
Some new weakly singular integral inequalities with discontinuous functions for two variables and their applications
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2288-9
New findings on exponential convergence of a Nicholson’s blowflies model with proportional delay
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2248-4
State bounding estimation for a linear continuous-time singular system with time-varying delay
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2065-9
New fixed point results in quasi-metric spaces and applications in fractals theory
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2119-Z
Existence and iteration of positive solution for fractional integral boundary value problems with p-Laplacian operator
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2317-8
Positive solutions of beam equations under nonlocal boundary value conditions
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2404-x
Dynamics of a stochastic phytoplankton-toxin phytoplankton–zooplankton model
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2251-9
Modeling and simulation of air pollutant distribution in street canyon area with Skytrain stations
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2382-z
Uniqueness of meromorphic solutions of the difference equation R1(z)f(z+1)+R2(z)f(z)=R3(z)$R_{1}(z)f(z+1)+R_{2}(z)f(z)=R_{3}(z)$
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2194-1
Predator–prey pattern formation driven by population diffusion based on Moore neighborhood structure
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2328-5
Random attractors for Ginzburg–Landau equations driven by difference noise of a Wiener-like process
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2165-6
Determining optimal policies for sugarcane harvesting in Thailand using bi-objective and quasi-Newton optimization methods
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2192-3
Synchronization of fractional-order dynamical network via aperiodically intermittent pinning control
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2109-1
Some results for sums of products of Chebyshev and Legendre polynomials
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2301-3
Preview tracking control for a class of fractional-order linear systems
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2403-y
A numerical study of oil spill prediction in the Gulf of Thailand using ocean wave model
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2206-1
Positive solutions for a boundary value problem of fractional differential equation with p-Laplacian operator
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2280-4
A stabilized coupled method and its optimal error estimates for elliptic interface problems
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2332-9
Blow-up for a degenerate and singular parabolic equation with a nonlocal source
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2219-9
Singular traveling wave solutions for Boussinesq equation with power law nonlinearity and dual dispersion
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2428-2
Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2375-y
Effect of insecticide on the population dynamics of brown planthoppers and Cyrtorhinus lividipennis: a modeling approach
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2128-Y
A stochastic predator–prey model for integrated pest management
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2291-1
Li–Yorke chaos on one-dimensional map lattices
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-1962-2
Nonoscillatory solutions for first-order neutral dynamic equations with continuously distributed delay on time scales
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2015-6
Meromorphic functions that share four or three small functions with their difference operators
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2116-2
On the boundedness of poles of generalized Padé approximants
来源期刊：Advances in Difference EquationsDOI：10.1186/S13662-019-2081-9
A delay differential equation model of mealybugs and green lacewings
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2226-x
Non-linear population discrete models with two time scales: re-scaling of part of the slow process
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2303-1
Complete monotonicity related to the k-polygamma functions with applications
来源期刊：Advances in Difference EquationsDOI：10.1186/s13662-019-2299-6
