scholarly journals Positive Solutions for Boundary Value Problems of Fractional Differential Equation with Integral Boundary Conditions

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Qiao Sun ◽  
Hongwei Ji ◽  
Yujun Cui
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Existence Results ◽  
Integral Boundary ◽  
Fractional Differential

By using two fixed-point theorems on cone, we discuss the existence results of positive solutions for the following boundary value problem of fractional differential equation with integral boundary conditions: D0+αx(t)+a(t)f(t,x(t))=0, t∈(0,1), x(0)=x′(0)=0, and x(1)=∫01x(t)dA(t).

scholarly journals Positive Solutions for BVP of Fractional Differential Equation with Integral Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Min Li ◽  
Jian-Ping Sun ◽  
Ya-Hong Zhao
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Fractional Differential Equation ◽  
Positive Solutions ◽  
Integral Boundary Conditions ◽  
Monotone Iterative Method ◽  
Nonlinear Fractional Differential Equation ◽  
Integral Boundary ◽  
Zero Function ◽  
Fractional Differential

In this paper, we consider a class of boundary value problems of nonlinear fractional differential equation with integral boundary conditions. By applying the monotone iterative method and some inequalities associated with Green’s function, we obtain the existence of minimal and maximal positive solutions and establish two iterative sequences for approximating the solutions to the above problem. It is worth mentioning that these iterative sequences start off with zero function or linear function, which is useful and feasible for computational purpose. An example is also included to illustrate the main result of this paper.

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