On existence of positive solutions for a class of discrete fractional boundary value problems
type: Item
instance of: scholarly article
title: On existence of positive solutions for a class of discrete fractional boundary value problems
zbMATH Open document ID: 1387.39008
author: Mujeeb ur Rehman
author: Faiza Iqbal
author: Arjumand Seemab
published in: Positivity
publication date: 2017-12-06T00:00:00Z
review text: The paper is concerned with the boundary value problem of a fractional difference equation \[ -\Delta^\nu_{\nu-2} u(t) =f(t+\nu-1,u(t+\nu-1)),\quad 1<\nu\leq 2,\quad t\in[0,N+1]\cap\mathbb{N}, \] \[ u(\nu-2)=0,\quad \Delta_{\nu-1}^{\nu-1}u(\nu+N)=0, \] where \(N\geq 2\) is an integer. The paper presents the corresponding Green's function and its properties. Then the Guo-Krasnoselskii fixed point theorem is used to establish the existence of at least one positive solutions of the above BVP.
reviewed by: Xueyan Liu
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 39A05
Mathematics Subject Classification ID: 39A99
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 6816291
zbMATH Keywords: discrete fractional calculus
zbMATH Keywords: fractional summation
zbMATH Keywords: fractional difference
MaRDI profile type: Publication
full work available at URL: s11117-016-0459-4
OpenAlex ID: W2559372665
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DOI: 10.1007/S11117-016-0459-4
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description: scientific article; zbMATH DE number 6816291