Publication detail

On dynamical systems with nabla half derivative on time scales

KISELA, T.

Original Title

On dynamical systems with nabla half derivative on time scales

Type

journal article in Web of Science

Language

English

Original Abstract

This paper is devoted to study of dynamical systems involving nabla half derivative on an arbitrary time scale. We prove existence and uniqueness of the solution of such system supplied with a suitable initial condition. Both Riemann–Liouville and Caputo approaches to noninteger-order derivatives are covered. Under special conditions we present an explicit form of the solution involving a time scales analogue of Mittag–Leffler function. Also an algorithm for solving of such problems on isolated time scales is established. Moreover, we show that half power functions are positive and decreasing with respect to t−s on an arbitrary time scale.

Keywords

Fractional calculus; time scales; nabla half derivative; dynamical systems; Mittag-Leffler function; existence and uniqueness

Authors

KISELA, T.

Released

23. 10. 2020

Publisher

Springer

ISBN

1660-5446

Periodical

Mediterranean Journal of Mathematics

Year of study

17

Number

187

State

Swiss Confederation

Pages from

1

Pages to

19

Pages count

19

URL

https://link.springer.com/article/10.1007/s00009-020-01629-w

BibTex

@article{BUT166026,
  author="Tomáš {Kisela}",
  title="On dynamical systems with nabla half derivative on time scales",
  journal="Mediterranean Journal of Mathematics",
  year="2020",
  volume="17",
  number="187",
  pages="1--19",
  doi="10.1007/s00009-020-01629-w",
  issn="1660-5446",
  url="https://link.springer.com/article/10.1007/s00009-020-01629-w"
}