On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions

HUANG Zhong-min, XIE Zuo-shi, HOU Cheng-min

doi:10.13371/j.cnki.chin.q.j.m.2014.04.009

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 4: 539 - 552

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.04.009

On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions

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1. Department of Mathematics, Yanbian University2. The School of Economics and International Trade, Zhejiang University of Finance and Economics

HOU Cheng-min(1963-), female, native of Yanji, Jilin, a professor of Yanbian University, M.S.D., engages in discrete dynamical system.

Received date: 2013-02-19

Online published: 2020-11-26

Supported by

Supported by the National Natural Science Foundation of China(11161049)；

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Abstract

In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green’s function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii’s fixed point theorem.

Key words： discrete fractional calculus; green's function; nonlocal fractional boundary conditions; existence of solution; fixed point

Cite this article

HUANG Zhong-min, XIE Zuo-shi, HOU Cheng-min . On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(4) : 539 -552 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.04.009

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