具有线性微分算子的分数阶微分方程积分边值问题

研究一类具有分数阶线性微分算子的非线性微分方程积分边值问题解的存在性与唯一性.利用Schauder不动点定理及压缩映射原理,建立并证明了边值问题解的存在性定理和唯一性定理,并给出两个例子以说明所得结论.     

一类具有Riemann-Liouville分数阶积分边值条件的奇异分数阶微分方程解的存在性

研究一类具有Riemann-Liouville分数阶积分边值条件的奇异分数阶微分方程解的存在性,其非线性项包含Caputo型分数阶导数,且在t=0具有奇异性.应用Schauder不动点定理获得了解的存在性定理,并给出了应用实例.     

基于Ph,e下Riemann-Liouville分数阶微分方程解的存在唯一性

利用基于集合P_h,e上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合P_h,e中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论.     

无限区间上多分数阶微分方程初值问题解的存在与唯一性

本文研究一类无限区间上具有Riemann-Liouville 导数的多分数阶非线性微分方程初值问题,在一类加权函数空间上使用Schauder 不动点定理建立了该问题解的存在性和唯一性结果, 举例说明了定理的应用.     

分数阶R-L微分方程初值问题解的存在唯一性

研究了R-L导数定义下的分数维微分方程初值问题解的存在性及其唯一性,给出了方程的Peano存在定理和不等式定理,基于逐次逼近的方法,利用对分数阶R-L微夯方程构造的Tonelli序列和Ascoli引理证明分数阶R-L微分方程解的存在性,根据分数阶不等式定理证明了分数阶R-L微分方程解的唯一性.     

具有逐项分数阶导数的微分方程边值问题解的存在性

研究了一类具有逐项分数阶导数的微分方程边值问题.对参数的各种取值情况进行了全面的分析,运用Banach压缩映射原理和Schauder不动点定理,得到并证明了边值问题解的存在性定理.最后,给出了两个例子来证明结论有效.     

分数阶微分方程的比较定理

本文给出了非线性Riemann—Liouville分数阶微分方程和Caputo分数阶微分方程与相应的非线性Volterra积分方程的等价性,并在此基础上建立了分数阶微分方程的比较定理．     

一类广义B-T方程边值问题解的存在性

研究一类含有两个分数阶导数的非线性分数阶微分方程在边值问题以及在边值非零情况下mild解的存在性,进而利用函数的初始值非零时Riemann-Liouville分数阶导数的奇异性,在加权连续函数空间上,运用Schauder不动点定理,得到关于这类问题的mild解存在的充分条件,完善和推广了某些已有结论.     

非线性分数阶微分方程三点边值问题解的存在性

讨论了一类非线性分数阶微分方程三点边值问题解的存在性.微分算子是Riemann-Liouville导算子并且非线性项依赖于低阶分数阶导数.通过将所考虑的问题转化为等价的Fredholm型积分方程,利用Schauder不动点定理获得该三点边值问题至少存在一个解.     

分数阶p-Laplacian边值问题正解的存在唯一性

运用Schauder不动点定理和上下解方法研究了一类分数阶p-Laplacian边值问题正解的存在性和唯一性,并给出了唯一解的迭代序列.     

Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative

In this paper, we shall discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann-Liouville sequential fractional derivative by using monotone iterative method.     

Impulsive periodic boundary value problems for fractional differential equation involving Riemann-Liouville sequential fractional derivative

In this paper, we investigate the existence of solutions of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville sequential fractional derivative by using monotone iterative method. An example is presented to illustrate our main result.     

Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative

In this paper, we shall discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of the solution of the periodic boundary value problem for a fractional differential equation involving a Riemann-Liouville fractional derivative by using the monotone iterative method.     

分数阶微分方程多点边值问题的正解

本文研究了在边界条件中含有多个分数导数项的分数阶微分方程多点边值问题多个正解的存在性.运用Green函数的性质以及有白-葛推导出的一般形式的Leggett-Williams不动点定理,建立了边值问题至少有三个正解存在的充分条件.最后,给出了一个例子,用于说明所得主要结论具有广泛的适用性.     

Properties of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations with a parameter

In this paper, by using fixed point theorems of concave operators in partial ordering Banach spaces, we establish the existence and uniqueness of positive solutions to a class of four-point boundary value problem of Caputo fractional differential equations for any given parameter. Moreover, we present some pleasant properties of positive solutions to the boundary value problem dependent on the parameter. In the end, two examples are given to illustrate our main results.     

非线性分数阶微分方程Robin型边值问题

In this paper,the existence and multiplicity of positive solutions for Robin type boundary value problem of differential equation involving the Riemann-Liouville fractional order derivative are established.     

一类分数阶微分方程边值问题三重正解的存在性

讨论了非线性分数阶微分方程的两点边值问题.其导数是Riemann-Liouville型分数阶导数,应用推广了的双锥不动点定理,证明其在L(0,1)中存在三重正解.     

The method of upper and lower solutions and impulsive fractional differential inclusions

In this paper the concept of lower and upper solutions combined with the fixed point theorem of Bohnnenblust–Karlin is used to investigate the existence of solutions for a class of the initial value problem for impulsive differential inclusions involving the Caputo fractional derivative.