Abstract and Applied Analysis

Positive and Nondecreasing Solutions to an m-Point Boundary Value Problem for Nonlinear Fractional Differential Equation

I. J. Cabrera, J. Harjani, and K. B. Sadarangani

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Abstract

We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D 0 + α u ( t ) + f ( t , u ( t ) ) = 0 ,    0 < t < 1 ,    2 < α 3 ,    u ( 0 ) = u ' ( 0 ) = 0 ,    u ' ( 1 ) = i = 1 m - 2 a i u ' ( ξ i ) , where D 0 + α denotes the standard Riemann-Liouville fractional derivative, f : [ 0,1 ] × [ 0 , ) [ 0 , ) is a continuous function, a i 0 for i = 1,2 , , m - 2 , and 0 < ξ 1 < ξ 2 < < ξ m - 2 < 1 . Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.

Article information

Source
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 826580, 15 pages.

Dates
First available in Project Euclid: 1 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364845185

Digital Object Identifier
doi:10.1155/2012/826580

Mathematical Reviews number (MathSciNet)
MR2872307

Zentralblatt MATH identifier
1234.34006

Citation

Cabrera, I. J.; Harjani, J.; Sadarangani, K. B. Positive and Nondecreasing Solutions to an m -Point Boundary Value Problem for Nonlinear Fractional Differential Equation. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 826580, 15 pages. doi:10.1155/2012/826580. https://projecteuclid.org/euclid.aaa/1364845185


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