Please use this identifier to cite or link to this item: http://hdl.handle.net/10773/25052
Title: Solutions of systems with the Caputo-Fabrizio fractional delta derivative on time scales
Author: Mozyrska, Dorota
Torres, Delfim F. M.
Wyrwas, Malgorzata
Keywords: Calculus on time scales
Caputo–Fabrizio fractional delta derivatives and integral
Exponential stability
Laplace transform on time scales
Existence and uniqueness of solution
Issue Date: May-2019
Publisher: Elsevier
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.
Peer review: yes
URI: http://hdl.handle.net/10773/25052
DOI: 10.1016/j.nahs.2018.12.001
ISSN: 1751-570X
Publisher Version: http://dx.doi.org/10.1016/j.nahs.2018.12.001
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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