TY - JOUR
ID - 505
TI - Fractional dynamical systems: A fresh view on the local qualitative theorems
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN -
AU - Sayevand, Khosro
AD - Faculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, Iran
Y1 - 2016
PY - 2016
VL - 7
IS - 2
SP - 303
EP - 318
KW - Fractional differential systems
KW - Stable manifold theorem
KW - Hartman-Grobman theorem
KW - Local center manifold theorem
KW - Local qualitative theory
DO - 10.22075/ijnaa.2016.505
N2 - The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of the local center manifold theorem, the stable manifold theorem and the Hartman-Grobman theorem to the scope of fractional differential systems. These latter two theorems establish that the qualitative behavior of the solution set of a nonlinear system of fractional differential equations near an equilibrium point is typically the same as the qualitative behavior of the solution set of the corresponding linearized system near the equilibrium point. Furthermore, we discuss the stability conditions for the equilibrium points of these systems. We point out that, the fractional derivative in these systems is in the Caputo sense.
UR - https://ijnaa.semnan.ac.ir/article_505.html
L1 - https://ijnaa.semnan.ac.ir/article_505_6dd6f750a1f5b7ac40e8c8f4e08ab830.pdf
ER -