ON A NEW CLASS OF ANALYTIC FUNCTION DERIVED BY A FRACTIONAL DIFFERENTIAL OPERATOR

Making use of the fractional differential operator, we impose and study a new class of analytic functions in the unit disk （type fractional differential equation）. The main object of this paper is to investigate inclusion relations, coefficient bound for this class. Moreover, we discuss some geometric properties of the fractional differential operator.     

EIGENVALUES OF STURM-LIOUVILLE OPERATOR WITH GENERAL BOUNDARY CONDITIONS

We study the asymptotic behavior for the eigenvalues of Sturm-Liouville operators with smooth potential.The precise asymptotic expressions for the eigenvalues of the operators with general boundary conditions are given.     

奇型Sturm-Liouville微分算子的极大增生扩张

应用扩展的Phillips理论及Brown和Krall关于共轭微分算式的构造原理,本文给出了奇型Sturm-Liouville 微分算子所有极大增生扩张的微分算式及定义域。     

EXISTENCE OF POSITIVE MULTIPLE SOLUTIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR

In this paper, we consider a two-point fractional boundary value problem. We provide sufficient conditions for the existence of multiple positive solutions to the boundary value problem by Krasnosel＇skii fixed point theorem on the cone.     

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR FRACTIONAL DIFFERENTIAL SYSTEM

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.     

一类多目标分式规划的二阶对称对偶问题

研究一类多目标分式规划的二阶对称对偶问题.在二阶F-凸性假设下给出了对偶问题的弱对偶、强对偶和逆对偶定理.并在对称和反对称假设下研究了该问题的自身对偶性.     

APPLICATION OF TWO OPERATORS TRANSFORM FROM CLASS A OPERATOR TO THE CLASS OF HYPONORMAL OPERATOR

In this article, we give an operator transform T (*) from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ(T ) = σ( T (*)) and σa(T )\{0} = σa( T (*))\{0}, in case T belongs to class A. Next, we obtain some relations between T and T (9).     

带有p-Laplace算子的分数阶边值问题的特征区间

本文研究了一类带有p-Laplace算子的分数阶微分方程两点边值问题.利用锥上的不动点定理,得到了这类边值问题的特征区间,推广了整数阶边值问题情形的结论.     

一类次线性分数微分方程的正解存在性

证明了一类非线性项受幂函数控制的次线性分数微分方程的正解存在性.主要方法是锥拉伸与锥压缩型的Krasnosel’skii不动点定理的局部应用.我们的结论表明该方程可以具有一个正解,只要非线性项在某个有界集上的“高度”是适当的.     

一类非线性算子方程的求解方法

1.引言首先研究线性方程Au=f (1.1)的求解问题,其中A是H→H的连续线性算子,H是可分Hilbert空间,U,f∈H,||f||=1.利用得到的结论,研究一类非线性算子方程AuBu+Cu=f(1.2)     

ON SOLVABILITY OF A BOUNDARY VALUE PROBLEM FOR A NONHOMOGENEOUS BIHARMONIC EQUATION WITH A BOUNDARY OPERATOR OF A FRACTIONAL ORDER

This paper is concerned with the solvability of a boundary value problem for a nonhomogeneous biharmonic equation. The boundary data is determined by a differential operator of fractional order in the Riemann-Liouville sense. The considered problem is a generalization of the known Dirichlet and Neumann problems.     

一类非线性算子方程的最小最大耦合拟解的存在性

摘要：本文利用半序方法。研究了一类非线性算子方程的最小最大耦合拟解的存在性。得到几个新的存在性定理，并且改进和推广了中相关结果．     

对称性对Schrodinger算子特征向量存在性的影响

讨论了sl2（C）中矩阵乘积的迹的性质；证明了离散Schrodinger算子H在其势Vn为Thue－Morse序列或准对称序列时，在空间Co（Z）内不存在特征向量．     

一类分数阶多项延迟微分方程的Jacobi谱配置方法

本文利用Jacobi谱配置方法数值求解了一类分数阶多项延迟微分方程,并证明了该方法是收敛的,通过若干数值算例验证了相应的理论结果,结果表明Jacobi谱配置方法求解这类方程是非常高效的,同时也为这类分数阶延迟微分方程的数值求解提供了新的选择,对分数阶泛函方程的数值方法的研究有一定的指导意义.     

EXISTENCE AND UNIQUENESS OF SOLUTIONS TO A CLASS OF NONLINEAR FRACTIONAL ORDER DIFFERENTIAL EQUATIONS WITH DELAY

A class of nonlinear fractional order differential equations with delay is investigated in this paper. Using Leray-Schauder fixed point theorem and the contraction mapping theorem, we obtain some sufficient conditions for the existence and uniqueness of solutions to the fractional order differential equations.     

非线性随机分数阶延迟积分微分方程Euler-Maruyama方法的强收敛性

本文研究了一类新的模型问题:非线性随机分数阶延迟积分微分方程.当方程中的漂移项和扩散项满足全局Lipschitz条件和线性增长条件时,基于压缩映射原理给出了该方程解存在唯一的充分条件.由于理论求解的困难,构造了一种数值方法(Euler-Maruyama方法),并证得强收敛阶为α-1/2,α∈(1/2,1].最后通过数值试验,验证了这一理论结果.     

THE BOUNDEDNESS FOR A CLASS OF ROUGH FRACTIONAL INTEGRAL OPERATORS ON VARIABLE EXPONENT LEBESGUE SPACES

In this paper,we will discuss the behavior of a class of rough fractional integral operators on variable exponent Lebesgue spaces,and establish their boundedness from L p 1 (·) (R n) to L p 2 (·) (R n).     

用Choi-Saigo-Srivastava算子定义的解析函数新子类

本文研究了用Choi-Saigo-Srivastava算子定义的一类解析函数.利用分析的方法和算子理论得到类中函数的积分表达式,偏差定理,卷积性质和半径问题.所得结果推广一些作者的相关结果.     

NUMERICAL SOLUTION OF THE SPACE FRACTIONAL DIFFERENTIAL EQUATION

In this paper, a space fractional differential equation is considered. The equation is obtained from the parabolic equation containing advection, diffusion and reaction terms by replacing the second order derivative in space by a fractional derivative in space of order. An implicit finite difference approximation for this equation is presented. The stability and convergence of the finite difference approximation are proved. A fractional-order method of lines is also presented. Finally, some numerical results are given.     

一类多目标半无限分式规划的最优性条件

<正>0引言分式规划作为最优化的一个分支,近年来,获得了很大的发展,如,文[4]利用(F,α,ρ,d)-凸函数,文[5]利用半局部预不变凸函数等分别讨论了相应的分式规划问题等,这些成果极大地推动了分式规划的发展.