Open Access Original research

The existence and uniqueness of solutions to boundary value problems of fractional difference equations

Yuanyuan Pan, Zhenlai Han*, Shurong Sun and Zhiqing Huang

Author Affiliations

School of Mathematical Sciences, University of Jinan, Shandong 250022, People’s Republic of China

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Mathematical Sciences 2012, 6:7 doi:10.1186/2251-7456-6-7

Published: 11 June 2012

Abstract

In this paper, we study the existence and uniqueness of solutions for the boundary value problem <a onClick="popup('http://www.iaumath.com/content/6/1/7/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.iaumath.com/content/6/1/7/mathml/M1">View MathML</a> where <a onClick="popup('http://www.iaumath.com/content/6/1/7/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.iaumath.com/content/6/1/7/mathml/M2">View MathML</a> is continuous, and nonnegative for <a onClick="popup('http://www.iaumath.com/content/6/1/7/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.iaumath.com/content/6/1/7/mathml/M3">View MathML</a> is a given function. We give a representation for the solution to this problem, and we prove the existence and uniqueness of solution to this problem by contraction mapping theorem and Brouwer theorem.

Keywords:
Discrete fractional equation; Boundary value problem; Existence and uniqueness of solution; Contraction mapping theorem; Brouwer theorem; Mathematics Subject Classification: 2010: 34A08; 34B18