# Advances in Difference Equations

## List of Papers (Total 2,995)

#### 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 multi-quasi...

#### 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.

#### Some properties of algebraic difference equations of first order

We prove that if g ( z ) $g(z)$ is a finite-order transcendental meromorphic solution of ( △ c g ( z ) ) 2 = A ( z ) g ( z ) g ( z + c ) + B ( z ) , $$\bigl(\triangle_{c} g(z)\bigr)^{2}=A(z)g(z)g(z+c)+B(z),$$ where A ( z ) $A(z)$ and B ( z ) $B(z)$ are polynomials such that deg A ( z ) > 0 $\deg A(z)>0$ , then 1 ≤ ρ ( g ) = max { λ ( g ) , λ ( 1 g ) } . 1 \leq\rho(g)=\max...

#### Weak solutions for a coupled system of Pettis-Hadamard fractional differential equations

In this paper, by applying the technique of measure of weak noncompactness and Mönch’s fixed point theorem, we investigate the existence of weak solutions under the Pettis integrability assumption for a coupled system of Hadamard fractional differential equations.

#### Stochastic Volterra integral equations with a parameter

In this paper, we study the properties of continuity and differentiability of solutions to stochastic Volterra integral equations and backward stochastic Volterra integral equations depending on a parameter.

#### Existence of almost periodic solution for neutral Nicholson blowflies model

This paper is concerned with a class of neutral Nicholson blowflies models with leakage delays and linear harvesting terms. Under appropriate conditions, some criteria are established for the existence and global exponential stability of almost periodic solutions for the model by applying exponential dichotomy theory. An example is provided to illustrate the effectiveness of the...

#### Nonlocal boundary value problems of fractional order at resonance with integral conditions

Based upon the well-known coincidence degree theory of Mawhin, we obtain some new existence results for a class of nonlocal fractional boundary value problems at resonance given by { D 0 + α u ( t ) = f ( t , u ( t ) , D 0 + α − 1 u ( t ) , D 0 + α − 2 u ( t ) ) , t ∈ ( 0 , 1 ) , I 0 + 3 − α u ( 0 ) = u ′ ( 0 ) = 0 , D 0 + β u ( 1 ) = ∫ 0 1 D 0 + β u ( t ) d A ( t...

#### Non-polynomial cubic spline discretization for system of non-linear singular boundary value problems using variable mesh

In this paper, we propose two generalized non-polynomial cubic spline schemes using a variable mesh to solve the system of non-linear singular two point boundary value problems. Theoretical analysis proves that the proposed methods have second- and third-order convergence. Both methods are applicable to singular boundary value problems. Numerical results are also provided to show...