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BAŠTINEC, J. DIBLÍK, J.
Original Title
Bounded solutions of discrete equations with several fractional differences
Type
conference paper
Language
English
Original Abstract
In the paper is considered a fractional discrete equation Sigma(s)(pi=1) Delta(beta pi) z(k + 1) = G(k)(k, z(k),..., z(k(0))), k = k(0), k(0) + 1,... where Delta(beta pi), beta(pi) > 0, pi = 1,..., s, are the beta(pi)-order fractional differences, G(k): {k} x Rk-k0+1 -> R, k(0) is an element of Z, k is an element of Z, k >= k(0) and z: {k(0), k(0) + 1,...} -> R. Sufficient conditions are given for the existence of bounded solutions satisfying inequalities b(k) < z(k) < c(k), for all k >= k(0) where b and c are real functions satisfying b(k) < c(k). An application is considered to an equation with several fractional differences Sigma(s)(pi=1) Delta(beta pi) z(k + 1) = G(k)(k, z(k),..., z(k(0))), k = k(0), k(0) + 1,... where xi is an element of R and sigma: {k(0), k(0) + 1,...}-> R. It is proved that there exists a bounded solution satisfying the inequality vertical bar z(k)vertical bar < L, k = k(0), k(0) + 1,..., for a constant L.
Keywords
discrete fractional equation; bounded solution; fractional difference
Authors
BAŠTINEC, J.; DIBLÍK, J.
Released
7. 6. 2024
Publisher
American Institute of Physics
Location
USA
ISBN
9780735449541
Book
AIP Conference Proceedings, Volume 3094, Issue 1, 7 June 2024, International Conference of Numerical Analysis and Applied Mathematics 2022, ICNAAM 2022
0094-243X
Periodical
AIP conference proceedings
Year of study
3094
Number
1
State
United States of America
Pages from
500044-1
Pages to
500044-4
Pages count
4
URL
https://pubs.aip.org/aip/acp/article-abstract/3094/1/500044/3297296/Bounded-solutions-of-discrete-equations-with?redirectedFrom=fulltext