fractional dynamical systems: a fresh view on the local qualitative theorems

نویسندگان

khosro sayevand

faculty of mathematical sciences, malayer university, p.o.box 16846-13114, malayer, iran

چکیده

the aim of this work is to describe the qualitative behavior of the solution set of a givensystem 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.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

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

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...

متن کامل

Fractional Dynamical Systems on Fractional Leibniz Algebroids

The theory of derivative of noninteger order goes back to Leibniz, Liouville, Riemann, Grunwald and Letnikov. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics, medicine.Classes of fractional differentiable systems have studied in [10], [4]. In the first section the fractional tangent bundle to a differentiable manifold is defined, u...

متن کامل

On the controllability of fractional dynamical systems

In the last three decades, interest in fractional calculus has experienced rapid growth and at present we can find many papers devoted its theoretical and application aspects (see the work of Machado et al. (2011) and the references therein). Fractional order models of real systems are often more adequate than the usually used integer order models in electrochemistry (Ichise et al., 1971), adve...

متن کامل

observational dynamical systems

چکیده در این پایاننامه ابتدا فضاهای متریک فازی را به صورت مشاهدهگرایانه بررسی میکنیم. فضاهای متریک فازی و توپولوژی تولید شده توسط این متریک معرفی شدهاند. سپس بر اساس فضاهایی که در فصل اول معرفی شدهاند آشوب توپولوژیکی، مینیمالیتی و مجموعههای متقاطع در شیوههای مختلف بررسی شده- اند. در فصل سوم مفهوم مجموعههای جاذب فازی به عنوان یک مفهوم پایهای در سیستمهای نیم-دینامیکی نسبی، تعریف شده است. ...

15 صفحه اول

jordan c-dynamical systems

in the first chapter we study the necessary background of structure of commutators of operators and show what the commutator of two operators on a separable hilbert space looks like. in the second chapter we study basic property of jb and jb-algebras, jc and jc-algebras. the purpose of this chapter is to describe derivations of reversible jc-algebras in term of derivations of b (h) which are we...

15 صفحه اول

Mean value theorems for Local fractional integrals on fractal space

In this paper, by some properties of Local fractional integral,we establish the generalized Mean value theorems for Local Fractional Integral.

متن کامل

منابع من

با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید


عنوان ژورنال:
international journal of nonlinear analysis and applications

جلد ۷، شماره ۲، صفحات ۳۰۳-۳۱۸

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023