Advances in Difference Equations

http://www.advancesindifferenceequations.com/

List of Papers (Total 2,959)

Solvability for a class of evolution equations of fractional order with nonlocal conditions on the half-line

In this paper, we get a new form equivalent integral equation for a class of evolution equations of fractional order with nonlocal conditions on the half-line. With the aid of it, the uniqueness of the mild solution is obtained by the Banach contraction theorem. Also, we present the existence and uniqueness theorem of positive mild solutions by the monotone iterative method without ...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent ...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the ...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent ...

General solution to a higher-order linear difference equation and existence of bounded solutions

We present a closed-form formula for the general solution to the difference equation x n + k − q n x n = f n , n ∈ N 0 , $$x_{n+k}-q_{n}x_{n}=f_{n},\quad n\in \mathbb {N}_{0}, $$ where k ∈ N $k\in \mathbb {N}$ , ( q n ) n ∈ N 0 $(q_{n})_{n\in \mathbb {N}_{0}}$ , ( f n ) n ∈ N 0 ⊂ C $(f_{n})_{n\in \mathbb {N}_{0}}\subset \mathbb {C}$ , in the case q n = q $q_{n}=q$ , n ∈ N 0 $n\in ...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the ...

Construction and solitary wave solutions of two-mode higher-order Boussinesq-Burger system

A new nonlinear partial differential system called two-mode higher-order Boussinesq-Burgers system is established. We aim to use the simplified bilinear method to find the necessary constraint conditions that guarantee the existence of both regular and singular multiple soliton solutions of the model. To study the correctness of the obtained results, we use the hyperbolic-tangent ...

On the fundamental solutions of a discontinuous fractional boundary value problem

The main purpose of this study is to investigate a fractional discontinuous Sturm-Liouville problem with transmission conditions. We shall consider a fractional boundary value problem involving an operator with two parts. It is shown that the eigenvalues and corresponding eigenfunctions of the main problem coincide with the eigenvalues and corresponding eigenfunctions of the ...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Feedback control effect on the Lotka-Volterra prey-predator system with discrete delays

In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control ...

Influence of cross-diffusion on the fecally-orally epidemic model with spatial heterogeneity

A strongly coupled cooperative parabolic system, which describes fecally-orally epidemic model with cross-diffusion in a heterogeneous environment, was formulated and analyzed. The basic reproduction number R 0 D $R_{0} ^{D}$ , which serves as a threshold parameter that predicts whether the coexistence will exist or not, is introduced by the next infection operator and the related ...

Stochastic regime switching SIS epidemic model with vaccination driven by Lévy noise

We formulate a stochastic SIS epidemic model with vaccination by introducing a Lévy noise and regime switching into the epidemic model. First, we prove that the stochastic model admits a unique global positive solution. Moreover, we study the asymptotic behavior of the stochastic regime switching SIS model with vaccination driven by Lévy noise.

Feedback control effect on the Lotka-Volterra prey-predator system with discrete delays

In this paper, we study a Lotka-Volterra prey-predator system with feedback control. We establish sufficient conditions under which a unique positive equilibrium is globally stable. Further, we show that a suitable feedback control on predator species can make prey species that is on the brink of extinction become globally stable, but under the conditions of small feedback control ...

Dynamical properties of a fractional reaction-diffusion trimolecular biochemical model with autocatalysis

In this paper, a reaction-diffusion trimolecular biochemical model with autocatalysis and fractional-order derivative is proposed. We establish the existence and uniqueness of a positive solution to this system in a Besov space. Besides, for this system, we obtain stability, Hopf and Turing bifurcations and spatial patterns. These dynamic behaviors of this system are slightly ...

A method for solving nonlinear Volterra’s population growth model of noninteger order

Many numerical methods have been developed for nonlinear fractional integro-differential Volterra’s population model (FVPG). In these methods, to approximate a function on a particular interval, only a restricted number of points have been employed. In this research, we show that it is possible to use the fuzzy transform method (F-transform) to tackle with FVPG. It makes the ...

Parameter estimation for nonergodic Ornstein-Uhlenbeck process driven by the weighted fractional Brownian motion

In this paper, we consider the nonergodic Ornstein-Uhlenbeck process X 0 = 0 , d X t = θ X t d t + d B t a , b , t ≥ 0 , $$ X_{0}=0, \quad\quad dX_{t}=\theta X_{t} \,dt+dB_{t}^{a,b},\quad t\geq0, $$ driven by the weighted fractional Brownian motion B t a , b $B_{t}^{a,b}$ with parameter a and b. Our goal is to estimate the unknown parameter θ > 0 $\theta>0$ based on the discrete ...

Global existence of solutions for a fractional Caputo nonlocal thermistor problem

We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem. Then additional existence and continuation theorems are obtained, ensuring global existence of solutions.

Multi-quasi-synchronization of coupled fractional-order neural networks with delays via pinning impulsive control

We investigate the collective dynamics of multi-quasi-synchronization of coupled fractional-order neural networks with delays. Using the pinning impulsive strategy, we design a novel controller to pin the coupled networks to realize the multi-quasi-synchronization. Based on the comparison principle and mathematical analysis, we derive some novel criteria of the ...

Optimality conditions for fractional variational problems with Caputo-Fabrizio fractional derivatives

In this paper, we study the necessary and sufficient optimality conditions for problems of the fractional calculus of variations with a Lagrange function depending on a Caputo-Fabrizio fractional derivative. The new kernel of Caputo-Fabrizio fractional derivative has no singularity, which is critical to interpreting the memory aftermath of the system. This property was not ...

Transmission dynamics of a Huanglongbing model with cross protection

Huanglongbing (HLB) is one of the most common widespread vector-borne transmission diseases through psyllid, which is called a kind of cancer of plant disease. In recent years, biologists have focused on the role of cross protection strategy to control the spread of HLB. In this paper, according to transmission mechanism of HLB, a deterministic model with cross protection is ...

On fractional Hahn calculus

In this paper, the new concepts of Hahn difference operators are introduced. The properties of fractional Hahn calculus in the sense of a forward Hahn difference operator are introduced and developed.