scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR A SINGULAR FRACTIONAL NONLINEAR DIFFERENTIAL EQUATION WITH FRACTIONAL INTEGRAL BOUNDARY CONDITIONS

2018 ◽  
Vol 26 (3) ◽  
pp. 469-482
Author(s):  
F. Gaafar
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fractional Integral ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Existence Of Positive Solutions

scholarly journals Positive Solutions for Fourth-Order Nonlinear Differential Equation with Integral Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Qi Wang ◽  
Yanping Guo ◽  
Yude Ji
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Nonlinear Differential Equation ◽  
Positive Solutions ◽  
Fourth Order ◽  
Integral Boundary Conditions ◽  
Integral Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Order Nonlinear Differential Equation ◽  
Existence And Nonexistence

This paper investigates the existence and nonexistence of positive solutions for a class of fourth-order nonlinear differential equation with integral boundary conditions. The associated Green's function for the fourth-order boundary value problems is first given, and the arguments are based on Krasnoselskii's fixed point theorem for operators on a cone.

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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