## List of Papers (Total 3,024)

#### Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method

We provide the numerical solution of a Volterra integro-differential equation of parabolic type with memory term subject to initial boundary value conditions. Finite difference method in combination with product trapezoidal integration rule is used to discretize the equation in time and sinc-collocation method is employed in space. A weakly singular kernel has been viewed as an...

#### 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...

#### A nonstandard finite difference scheme for a multi-group epidemic model with time delay

In this paper, we derive a discretized multi-group epidemic model with time delay by using a nonstandard finite difference (NSFD) scheme. A crucial observation regarding the advantage of the NSFD scheme is that the positivity and boundedness of solutions of the continuous model are preserved. Furthermore, we show that the discrete model has the same equilibria, and the conditions...

#### 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.