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Fractional dynamical systems: A fresh view on the local qualitative theorems | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 25، دوره 7، شماره 2، اسفند 2016، صفحه 303-318 اصل مقاله (398.53 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2016.505 | ||
| نویسنده | ||
| Khosro Sayevand* | ||
| Faculty of Mathematical Sciences, Malayer University, P.O.Box 16846-13114, Malayer, Iran | ||
| تاریخ دریافت: 16 بهمن 1394، تاریخ بازنگری: 25 مرداد 1395، تاریخ پذیرش: 12 مهر 1395 | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Fractional differential systems؛ Stable manifold theorem؛ Hartman-Grobman theorem؛ Local center manifold theorem؛ Local qualitative theory | ||
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