Existence of Positive Solutions for a Functional Fractional Boundary Value Problem

Chuanzhi Bai

doi:10.1155/2010/127363

Abstract

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

Highlights

Fractional differential equations can describe many phenomena in various fields of science and engineering such as physics, mechanics, chemistry, control, and engineering
The following lemma is crucial in finding an integral representation of the boundary value problem 1.3 – 1.5
In the sequel we will denote by C0 0, 1 the space of all continuous functions x : 0, 1 → R with x 0 0

Summary

Introduction

Fractional differential equations can describe many phenomena in various fields of science and engineering such as physics, mechanics, chemistry, control, and engineering. As pointed out in 16 , boundary value problems associated with functional differential equations have arisen from problems of physics and variational problems of control theory appeared early in the literature; see 17, 18. Since many authors see, e.g., 19–23 investigated the existence of solutions for boundary value problems concerning functional differential equations. An increasing interest in studying the existence of solutions for boundary value problems of fractional-order functional differential equations is observed; see for example, 24–26. Au ≥ u , u ∈ K ∩ ∂Ω1, Au ≤ u , u ∈ K ∩ ∂Ω2, A has a fixed point in K ∩ Ω2 \ Ω1

Preliminaries

Main Result

Γρ q gk M

An Example