## Abstract and Applied Analysis

### Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations

#### Abstract

We study some existence results in a Banach space for a nonlocal boundary value problem involving a nonlinear differential equation of fractional order $q$ given by $^{c}{D}^{q}x(t)=f(t,x(t))$, $0 \lt t \lt 1$, $q\in (m-1,m]$, $m\in \mathbb{N}$, $m\geq 2$, $x(0)=0$, ${x}^{\prime}(0)=0,\,{x}^{\prime \prime }(0)=0,\ldots ,{x}^{(m-2)}(0)=0$, $x(1)=\alpha x(\eta )$. Our results are based on the contraction mapping principle and Krasnoselskii's fixed point theorem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2009 (2009), Article ID 494720, 9 pages.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1268745574

Digital Object Identifier
doi:10.1155/2009/494720

Mathematical Reviews number (MathSciNet)
MR2516016

Zentralblatt MATH identifier
1186.34009

#### Citation

Ahmad, Bashir; Nieto, Juan J.; Eloe, Paul. Existence of Solutions for Nonlocal Boundary Value Problems of Higher-Order Nonlinear Fractional Differential Equations. Abstr. Appl. Anal. 2009 (2009), Article ID 494720, 9 pages. doi:10.1155/2009/494720. https://projecteuclid.org/euclid.aaa/1268745574

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