scholarly journals Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Chuanzhi Bai
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fractional Order ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Existence Results ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Functional Differential

We study the existence of positive solutions for a boundary value problem of fractional-order functional differential equations. Several new existence results are obtained.

scholarly journals Some results on boundary value problems for functional differential equations

1996 ◽  
Vol 19 (2) ◽  
pp. 335-342
Author(s):  
P. Ch. Tsamatos ◽  
S. K. Ntouyas
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
A Priori ◽  
Functional Differential Equations ◽  
Existence Results ◽  
A Priori Bounds ◽  
Nonlinear Alternative ◽  
Functional Differential

Existence results for a second order boundary value problem for functional differential equation, are givn. The results are based on the nonlinear Alternative, of Leray-Schauder and rely on a priori bounds on solutions. These results are generalizations of recent results from ordinary differential equations and complete our earlier results on the same problem.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

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