Publication detail

On dynamical systems with nabla half derivative on time scales

KISELA, T.

English title

On dynamical systems with nabla half derivative on time scales

Type

journal article in Web of Science

Language

en

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.

English 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 in English

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

Released

23.10.2020

Publisher

Springer

ISSN

1660-5446

Volume

17

Number

187

Pages from–to

1–19

Pages count

19

BIBTEX


@article{BUT166026,
  author="Tomáš {Kisela} and Jan {Čermák},
  title="On dynamical systems with nabla half derivative on time scales",
  year="2020",
  volume="17",
  number="187",
  month="October",
  pages="1--19",
  publisher="Springer",
  issn="1660-5446"
}