Detail publikace

On dynamical systems with nabla half derivative on time scales

KISELA, T.

Originální název

On dynamical systems with nabla half derivative on time scales

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

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

Autoři

KISELA, T.

Vydáno

23. 10. 2020

Nakladatel

Springer

ISSN

1660-5446

Periodikum

Mediterranean Journal of Mathematics

Ročník

17

Číslo

187

Stát

Švýcarská konfederace

Strany od

1

Strany do

19

Strany počet

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"
}