TY - JOUR
T1 - Variable order fractional systems
AU - Ortigueira, Manuel D.
AU - Valério, Duarte
AU - Machado, J. Tenreiro
N1 - info:eu-repo/grantAgreement/FCT/5876/147324/PT#
info:eu-repo/grantAgreement/FCT/5876/147353/PT#
SFRH/BSAB/142920/2018.
Sem PDF conforme despacho.
PY - 2019/6/15
Y1 - 2019/6/15
N2 - Fractional Calculus had a remarkable evolution during recent decades, and paved the way towards the definition of variable order derivatives. In the literature we find several different alternative definitions of such operators. This paper presents an overview of the fundamentals of this topic and addresses the questions of finding out which of them are reasonable according to simple criteria used for constant order fractional derivatives. This approach leads to the definitions of variable order fractional derivative based on the Grünwald–Letnikov and the Liouville formulations defined on R, as well as to the definition of a Mittag-Leffler function for variable orders, and to the application of these definitions to dynamical systems.
AB - Fractional Calculus had a remarkable evolution during recent decades, and paved the way towards the definition of variable order derivatives. In the literature we find several different alternative definitions of such operators. This paper presents an overview of the fundamentals of this topic and addresses the questions of finding out which of them are reasonable according to simple criteria used for constant order fractional derivatives. This approach leads to the definitions of variable order fractional derivative based on the Grünwald–Letnikov and the Liouville formulations defined on R, as well as to the definition of a Mittag-Leffler function for variable orders, and to the application of these definitions to dynamical systems.
KW - Fractional derivative
KW - Fractional integral
KW - Variable order
KW - Variable order linear system
KW - Variable order Mittag-Leffler function
UR - http://www.scopus.com/inward/record.url?scp=85058019999&partnerID=8YFLogxK
U2 - 10.1016/j.cnsns.2018.12.003
DO - 10.1016/j.cnsns.2018.12.003
M3 - Article
AN - SCOPUS:85058019999
SN - 1007-5704
VL - 71
SP - 231
EP - 243
JO - Communications In Nonlinear Science And Numerical Simulation
JF - Communications In Nonlinear Science And Numerical Simulation
ER -