Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Dorota Mozyrska , Delfim F.M. Torres , Małgorzata Wyrwas

Abstract

Caputo–Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo–Fabrizio fractional derivative is recovered. For isolated or partly continuous and partly discrete, i.e., hybrid time scales, one gets new fractional operators. We concentrate on the behavior of solutions to initial value problems with the Caputo–Fabrizio fractional delta derivative on an arbitrary time scale. In particular, the exponential stability of linear systems is studied. A necessary and sufficient condition for the exponential stability of linear systems with the Caputo–Fabrizio fractional delta derivative on time scales is presented. By considering a suitable fractional dynamic equation and the Laplace transform on time scales, we also propose a proper definition of Caputo–Fabrizio fractional integral on time scales. Finally, by using the Banach fixed point theorem, we prove existence and uniqueness of solution to a nonlinear initial value problem with the Caputo–Fabrizio fractional delta derivative on time scales.
Author Dorota Mozyrska (FCS / DM)
Dorota Mozyrska,,
- Department of Mathematics
, Delfim F.M. Torres
Delfim F.M. Torres,,
-
, Małgorzata Wyrwas (FCS / DM)
Małgorzata Wyrwas,,
- Department of Mathematics
Journal seriesNonlinear Analysis-Hybrid Systems, [Nonlinear Analysis: Hybrid Systems], ISSN 1751-570X, e-ISSN 1878-7460, (N/A 140 pkt)
Issue year2019
Vol32
Pages168-176
Publication size in sheets0.5
Keywords in EnglishCalculus on time scales, Caputo–Fabrizio fractional delta derivatives and integral, Exponential stability, Laplace transform on time scales, Existence and uniqueness of solution
ASJC Classification1706 Computer Science Applications; 2207 Control and Systems Engineering; 2603 Analysis
DOIDOI:10.1016/j.nahs.2018.12.001
Internal identifierROC 19-20
Languageen angielski
Score (nominal)140
Score sourcejournalList
ScoreMinisterial score = 140.0, 26-03-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.663; WoS Impact Factor: 2018 = 5.266 (2) - 2018=5.016 (5)
Citation count*5 (2020-03-27)
Cite
Share Share

Get link to the record


* presented citation count is obtained through Internet information analysis and it is close to the number calculated by the Publish or Perish system.
Back
Confirmation
Are you sure?