Fractional dynamical systems: A fresh view on the local qualitative theorems

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SAYEVAND KHOSRO

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS Year:2016 | Volume:7 | Issue:2 Page(s): 303-318

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Title

Fractional dynamical systems: A fresh view on the local qualitative theorems

Author(s)

SAYEVAND KHOSRO | Issue Writer Certificate

Keywords

Fractional differential systems

Stable manifold theorem

Hartman-Grobman theorem

Local center manifold theorem

Local qualitative theory

Abstract

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.

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APA: Copy

SAYEVAND, KHOSRO. (2016). Fractional dynamical systems: A fresh view on the local qualitative theorems. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 7(2), 303-318. SID. https://sid.ir/paper/340727/en

Vancouver: Copy

SAYEVAND KHOSRO. Fractional dynamical systems: A fresh view on the local qualitative theorems. INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS[Internet]. 2016;7(2):303-318. Available from: https://sid.ir/paper/340727/en

IEEE: Copy

KHOSRO SAYEVAND, “Fractional dynamical systems: A fresh view on the local qualitative theorems,” INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol. 7, no. 2, pp. 303–318, 2016, [Online]. Available: https://sid.ir/paper/340727/en

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