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# Analysis

### International mathematical journal of analysis and its applications

CiteScore 2018: 0.72

SCImago Journal Rank (SJR) 2018: 0.363
Source Normalized Impact per Paper (SNIP) 2018: 0.530

Mathematical Citation Quotient (MCQ) 2018: 0.36

Online
ISSN
2196-6753
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Volume 35, Issue 2

# On positive solutions to fractional difference inclusions

Rui A. C. Ferreira
/ Christopher S. Goodrich
Published Online: 2015-03-19 | DOI: https://doi.org/10.1515/anly-2012-1281

## Abstract

In this paper we consider a fractional difference inclusion of the form $\left({\phantom{\rule{0.166667em}{0ex}}}_{\alpha -1}{\Delta }^{\alpha }y\right)\left(t\right)\in \lambda y\left(t+\alpha -1\right)+f\left(t+\alpha -1,y\left(t+\alpha -1\right)\right)$, $y\left(\alpha -1\right)=y\left(\alpha -1+T\right)+{\sum }_{j=1}^{N}{F}_{j}\left(y\left({t}_{j}\right)\right)$, where $0<\alpha <1$. Consequently, we treat the situation in which the boundary condition is both nonlocal and nonlinear. Thus, the boundary conditions under study can be very general. We provide conditions under which this problem has at least one positive solution and then discuss the application of the results. Finally, since we allow ${F}_{j}\equiv 0$, for each j, our results are also new for the case of periodic boundary conditions.

MSC: 26A33; 34A60; 39A12; 39A99; 65Q10

Revised: 2014-12-25

Accepted: 2015-02-15

Published Online: 2015-03-19

Published in Print: 2015-05-01

Funding Source: FEDER

Award identifier / Grant number: COMPETE, Programa Operacional Factores de Competitividade

Funding Source: Portuguese Foundation for Science and Technology

Award identifier / Grant number: PEst-C/MAT/UI4106/2011, FCOMP-01-0124-FEDER-022690

Citation Information: Analysis, Volume 35, Issue 2, Pages 73–83, ISSN (Online) 2196-6753, ISSN (Print) 0174-4747,

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