Publication detail

Bounded solutions to systems of fractional discrete equations

DIBLÍK, J.

Original Title

Bounded solutions to systems of fractional discrete equations

Type

journal article in Web of Science

Language

English

Original 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.

Keywords

Fractional discrete difference; asymptotic behavior; system of fractional discrete equations; estimates of solutions

Authors

DIBLÍK, J.

Released

19. 7. 2022

Publisher

De Gruyter

ISBN

2191-950X

Periodical

Advances in Nonlinear Analysis

Year of study

11

Number

1

State

Federal Republic of Germany

Pages from

1614

Pages to

1630

Pages count

17

URL

https://www.degruyter.com/document/doi/10.1515/anona-2022-0260/html

Full text in the Digital Library

http://hdl.handle.net/11012/208201

BibTex

@article{BUT178596,
  author="Josef {Diblík}",
  title="Bounded solutions to systems of fractional discrete equations",
  journal="Advances in Nonlinear Analysis",
  year="2022",
  volume="11",
  number="1",
  pages="1614--1630",
  doi="10.1515/anona-2022-0260",
  issn="2191-950X",
  url="https://www.degruyter.com/document/doi/10.1515/anona-2022-0260/html"
}