Positive solutions to singular fractional differential system with coupled boundary conditions

By using the fixed point theory in cone and constructing some available integral operators together with approximating technique, the existence of positive solution for a singular nonlinear semipositone fractional differential system with coupled boundary conditions is established. Two examples are then given to demonstrate the validity of our main results.     

Positive solutions for Dirichlet problems of singular nonlinear fractional differential equations

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: Dαu(t)+f(t,u(t),Dμu(t))=0, u(0)=u(1)=0, where 1<α<2, 0<μ?α−1, Dα is the standard Riemann-Liouville fractional derivative, f is a positive Carathéodory function and f(t,x,y) is singular at x=0. By means of a fixed point theorem on a cone, the existence of positive solutions is obtained. The proofs are based on regularization and sequential techniques.     

Existence of solutions for fractional differential equations with multi-point boundary conditions

We discuss the existence of solutions for a nonlinear multi-point boundary value problem of integro-differential equations of fractional order q ∈ (1, 2]. Our analysis relies on the contraction mapping principle and the Krasnoselskii’s fixed point theorem. Example is provided to illustrate the theory.     

含积分边界条件的分数阶微分方程边值问题的正解的存在性

研究了含积分边界条件的分数阶微分方程的边值问题,首先给出格林函数及性质,其次将问题转化为一个等价的积分方程,最后应用Krasnoselkii及Leggett-Williams不动点定理得到了一个及多个正解的存在性,推广了以往的结果．     

Existence of positive solution for singular fractional differential equation

In this paper, we establish the existence of a positive solution to a singular boundary value problem of nonlinear fractional differential equation. Our analysis rely on nonlinear alternative of Leray-Schauder type and Krasnoselskii’s fixed point theorem in a cone.     

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.     

Positive solutions for a class of fractional differential equations with integral boundary conditions

The existence of positive solutions for a class of fractional equations involving the Riemann–Liouville fractional derivative with integral boundary conditions is investigated. By means of the monotone iteration method and some inequalities associated with the Green function, we obtain the existence of a positive solution and establish the iterative sequence for approximating the solution.     

Positive solutions of singular third-order three-point boundary value problem

In this paper we investigate the problem of existence of positive solutions for the nonlinear singular third-order three-point boundary value problem

     

一类分数阶微分方程组积分边值问题的正解

利用锥拉伸和压缩不动点定理,研究了一类具有Riemann-Liouvile分数阶积分条件的分数阶微分方程组边值问题.结合该问题相应Green函数的性质,获得了其正解的存在性条件,并给出了一些应用实例.     

Positive solutions for singular boundary value problems of a coupled system of differential equations

By using fixed point theorem of cone expansion and compression, this paper investigates the existence of multiple positive solutions for singular boundary value problems of a coupled system of nonlinear ordinary differential equations.     

Positive solutions of nonlinear singular third-order two-point boundary value problem

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem

     

Positive solutions for boundary value problem of nonlinear fractional differential equation

In this paper, we investigate the existence and multiplicity of positive solutions for nonlinear fractional differential equation boundary value problem:

     

具p-Laplace算子的分数阶微分方程边值问题的正解

考虑具有p-Laplace算子的分数阶泛函微分方程边值问题,利用锥上的不动点定理,得到了其正解及多个正解存在的充分条件,所得结果推广了已有的结论,并举例说明了结论的适用性.     

一类分数阶微分方程积分边值问题正解的分歧性

利用分歧方法和拓扑度理论,研究了一类带参数的分数阶微分方程积分边值问题正解的存在性.根据格林函数的性质,得到了系统正解的存在的若干充分条件.最后,通过数值例子验证了所得结果的有效性.     

The existence of a positive solution for a singular coupled system of nonlinear fractional differential equations

In this paper we establish the existence of a positive solution to a singular coupled system of nonlinear fractional differential equations. Our analysis rely on a nonlinear alternative of Leray–Schauder type and Krasnoselskii’s fixed point theorem in a cone.