Abstract and Applied Analysis

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

Bashir Ahmad, Juan J. Nieto, and Paul Eloe

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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 < t < 1 , q ( m 1 , m ] , m , m 2 ,  x ( 0 ) = 0 ,  x ( 0 ) = 0 ,  x ′′ ( 0 ) = 0 , , x ( m 2 ) ( 0 ) = 0 , x ( 1 ) = α x ( η ) . 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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