Positive solutions for boundary value problem of nonlinear fractional functional differential equations

2011 ◽  
Vol 217 (22) ◽  
pp. 9278-9285 ◽  
Author(s):  
Xiaoyan Li ◽  
Song Liu ◽  
Wei Jiang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

scholarly journals The Existence of Solutions for Boundary Value Problem of Fractional Functional Differential Equations with Delay

2018 ◽  
Vol 228 ◽  
pp. 01005
Author(s):  
Mengrui Xu ◽  
Yanan Li ◽  
Yige Zhao ◽  
Shurong Sun
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Contraction Mapping Principle ◽  
Alternative Theorem ◽  
Nonlinear Alternative ◽  
Banach Contraction ◽  
Functional Differential ◽  
Fractional Functional Differential Equations ◽  
Fractional Functional

A class of boundary value problem for fractional functional differential equation with delay $ \left\{ {\begin{array}{*{20}c} {^{C} D^{\sigma } \omega (t) = f(t,\omega _{t} ),t \in [0,\zeta ],} \\ {\omega (0) = 0,\,\omega ^{\prime}(0) = 0,\,\omega ^{\prime\prime}(\zeta ) = 1,} \\ \end{array} } \right. $ is studied, where $ 2 < \sigma \le 3,\,\,^{c} D^{\sigma } $ devote standard Caputo fractional derivative. In this article, three new criteria on existence and uniqueness of solution are obtained by Banach contraction mapping principle, Schauder fixed point theorem and nonlinear alternative theorem.

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.

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