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

• Main Authors: I. J. Cabrera, J. Harjani, K. B. Sadarangani
• Format: Article
• Language: English
• Published: Hindawi Limited 2012-01-01
• Series: Abstract and Applied Analysis
• Online Access: http://dx.doi.org/10.1155/2012/826580
• ISSN: 1085-3375; 1687-0409

We are concerned with the existence and uniqueness of a positive and nondecreasing solution for the following nonlinear fractional m-point boundary value problem: D0+αu(t)+f(t,u(t))=0,  0<t<1,  2<α≤3,  u(0)=u'(0)=0,  u'(1)=∑i=1m-2aiu'(ξi), where D0+α denotes the standard Riemann-Liouville fractional derivative, f:[0,1]×[0,∞)→[0,∞) is a continuous function, ai≥0 for i=1,2,…,m-2, and 0<ξ1<ξ2<⋯<ξm-2<1. Our analysis relies on a fixed point theorem in partially ordered sets. Some examples are also presented to illustrate the main results.