Detail publikace
On dynamical systems with nabla half derivative on time scales
KISELA, T.
Anglický název
On dynamical systems with nabla half derivative on time scales
Typ
článek v časopise ve Web of Science, Jimp
Jazyk
en
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.
Anglický 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 anglicky
Fractional calculus; time scales; nabla half derivative; dynamical systems; Mittag-Leffler function; existence and uniqueness
Vydáno
23.10.2020
Nakladatel
Springer
ISSN
1660-5446
Ročník
17
Číslo
187
Strany od–do
1–19
Počet stran
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"
}