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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

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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


In this paper we consider a fractional difference inclusion of the form (α-1Δαy)(t)λy(t+α-1)+f(t+α-1,y(t+α-1)), y(α-1)=y(α-1+T)+j=1NFj(y(tj)), where 0<α<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 Fj0, for each j, our results are also new for the case of periodic boundary conditions.

Keywords: Discrete fractional calculus; difference inclusion; positive solution; fixed point index; nonlocal boundary conditions

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

About the article

Received: 2014-08-14

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: University of Aveiro, Center for Research and Development in Mathematics and Applications

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, DOI: https://doi.org/10.1515/anly-2012-1281.

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