Publication detail

Bounded solutions of discrete equations with several fractional differences

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

ISBN

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