Bounded solutions to systems of fractional discrete equations

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dc.contributor.authorDiblĂ­k, Josefcs
dc.coverage.issue1cs
dc.coverage.volume11cs
dc.date.issued2022-07-19cs
dc.description.abstractThe article is concerned with systems of fractional discrete equations Delta(alpha)x(n + 1) = F-n(n, x(n), x(n - 1), ..., x(n(0))), n = n(0), n(0) + 1, ..., where n(0) is an element of Z , n is an independent variable, Delta(alpha) is an alpha-order fractional difference, alpha is an element of R, F-n : {n} x Rn-n0+1 -> R-s, S >= 1 is a fixed integer, and x : {n(0), n(0) + 1, ...} -> R-s is a dependent (unknown) variable. A retract principle is used to prove the existence of solutions with graphs remaining in a given domain for every n >= n(0), which then serves as a basis for further proving the existence of bounded solutions to a linear nonhomogeneous system of discrete equations Delta(alpha)x(n + 1) = A(n)x(n) + delta(n), n = n(0), n(0) + 1, ..., where A(n) is a square matrix and delta(n) is a vector function. Illustrative examples accompany the statements derived, possible generalizations are discussed, and open problems for future research are formulated as well.en
dc.description.abstractThe article is concerned with systems of fractional discrete equations Delta(alpha)x(n + 1) = F-n(n, x(n), x(n - 1), ..., x(n(0))), n = n(0), n(0) + 1, ..., where n(0) is an element of Z , n is an independent variable, Delta(alpha) is an alpha-order fractional difference, alpha is an element of R, F-n : {n} x Rn-n0+1 -> R-s, S >= 1 is a fixed integer, and x : {n(0), n(0) + 1, ...} -> R-s is a dependent (unknown) variable. A retract principle is used to prove the existence of solutions with graphs remaining in a given domain for every n >= n(0), which then serves as a basis for further proving the existence of bounded solutions to a linear nonhomogeneous system of discrete equations Delta(alpha)x(n + 1) = A(n)x(n) + delta(n), n = n(0), n(0) + 1, ..., where A(n) is a square matrix and delta(n) is a vector function. Illustrative examples accompany the statements derived, possible generalizations are discussed, and open problems for future research are formulated as well.en
dc.formattextcs
dc.format.extent1614-1630cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationAdvances in Nonlinear Analysis. 2022, vol. 11, issue 1, p. 1614-1630.en
dc.identifier.doi10.1515/anona-2022-0260cs
dc.identifier.issn2191-9496cs
dc.identifier.orcid0000-0001-5009-316Xcs
dc.identifier.other178596cs
dc.identifier.researcheridD-3530-2014cs
dc.identifier.scopus6701633618cs
dc.identifier.urihttp://hdl.handle.net/11012/208201
dc.language.isoencs
dc.publisherDe Gruytercs
dc.relation.ispartofAdvances in Nonlinear Analysiscs
dc.relation.urihttps://www.degruyter.com/document/doi/10.1515/anona-2022-0260/htmlcs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2191-9496/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectFractional discrete differenceen
dc.subjectasymptotic behavioren
dc.subjectsystem of fractional discrete equationsen
dc.subjectestimates of solutionsen
dc.subjectFractional discrete difference
dc.subjectasymptotic behavior
dc.subjectsystem of fractional discrete equations
dc.subjectestimates of solutions
dc.titleBounded solutions to systems of fractional discrete equationsen
dc.title.alternativeBounded solutions to systems of fractional discrete equationsen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-178596en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 15:17:43en
sync.item.modts2025.10.14 09:46:45en
thesis.grantorVysoké učení technické v Brně. Středoevropský technologický institut VUT. Kybernetika a robotikacs
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