## Bounded solutions to systems of fractional discrete equations

 dc.contributor.author DiblĂ­k, Josef cs dc.coverage.issue 1 cs dc.coverage.volume 11 cs dc.date.accessioned 2022-07-27T14:53:12Z dc.date.available 2022-07-27T14:53:12Z dc.date.issued 2022-07-19 cs dc.description.abstract The 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.format text cs dc.format.extent 1614-1630 cs dc.format.mimetype application/pdf cs dc.identifier.citation Advances in Nonlinear Analysis. 2022, vol. 11, issue 1, p. 1614-1630. en dc.identifier.doi 10.1515/anona-2022-0260 cs dc.identifier.issn 2191-950X cs dc.identifier.other 178596 cs dc.identifier.uri http://hdl.handle.net/11012/208201 dc.language.iso en cs dc.publisher De Gruyter cs dc.relation.ispartof Advances in Nonlinear Analysis cs dc.relation.uri https://www.degruyter.com/document/doi/10.1515/anona-2022-0260/html cs dc.rights Creative Commons Attribution 4.0 International cs dc.rights.access openAccess cs dc.rights.sherpa http://www.sherpa.ac.uk/romeo/issn/2191-950X/ cs dc.rights.uri http://creativecommons.org/licenses/by/4.0/ cs dc.subject Fractional discrete difference en dc.subject asymptotic behavior en dc.subject system of fractional discrete equations en dc.subject estimates of solutions en dc.title Bounded solutions to systems of fractional discrete equations en dc.type.driver article en dc.type.status Peer-reviewed en dc.type.version publishedVersion en sync.item.dbid VAV-178596 en sync.item.dbtype VAV en sync.item.insts 2022.08.21 00:54:34 en sync.item.modts 2022.08.21 00:15:08 en thesis.grantor VysokĂ© uÄŤenĂ­ technickĂ© v BrnÄ›. StĹ™edoevropskĂ˝ technologickĂ˝ institut VUT. Kybernetika a robotika cs
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