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Attractors of Caputo fractional differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Attractors of Caputo fractional differential equationsby Thai Son Doan, Peter E. Kloeden, Hoang The Tuan.
Author:	Doan, Thai Son.
other author:	Kloeden, Peter E.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xi, 140 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Fractional differential equations.
Online resource:	https://doi.org/10.1007/978-3-032-05511-8
ISBN:	9783032055118$q(electronic bk.)

Attractors of Caputo fractional differential equations
Doan, Thai Son.

Attractors of Caputo fractional differential equations[electronic resource] /by Thai Son Doan, Peter E. Kloeden, Hoang The Tuan. - Cham :Springer Nature Switzerland :2025. - xi, 140 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8201. - SpringerBriefs in mathematics..

Preface -- Introduction -- Useful Inequalities -- Existence and Uniqueness of Solutions -- Linear Systems of Caputo FDEs -- Asymptotic Stability and instability -- Lyapunov Functions -- Non-Intersecting Solutions -- Caputo Dynamical Systems -- Dissipative Caputo FDEs -- Attractors of Scalar Caputo FDEs -- Attractors of Caputo Semi-Groups -- References.

This book focuses on dissipative Caputo fractional differential equations (FDEs) with an autonomous vector field. The introduction of Caputo FDEs in the 1960s allowed initial value problems to be handled more naturally and the asymptotic behaviour of models based on them to be investigated by researchers. More recently, mathematically defined dynamical systems generated by Caputo FDEs and their attractors have been introduced. Dissipative Caputo FDEs have vector fields which satisfy a dissipativity property. For ordinary differential equations (ODEs) it follows from such a property that an absorbing set exists which contains all the long-term dynamical behaviour of the system such as the existence of an attractor. The situation is more complicated for Caputo FDEs, since these are essentially integral equations, and the dissipative inequalities cannot be so easily exploited. Moreover, such integral equations are essentially nonautonomous due to the form of the kernel in the integral equations, even when the vector field is "autonomous," i.e., does not depend explicitly on time. The book is based on recent results of the three coauthors in various combinations with each other and with their other coauthors, in particular Nguyen Dinh Cong and Hieu Trinh. The main aim is to develop and present a theory of dynamical systems and their attractors for Caputo FDEs.

ISBN: 9783032055118$q(electronic bk.)

Standard No.: 10.1007/978-3-032-05511-8doiSubjects--Topical Terms:

709091
Fractional differential equations.

LC Class. No.: QA372

Dewey Class. No.: 515.35

Attractors of Caputo fractional differential equations
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520 $a This book focuses on dissipative Caputo fractional differential equations (FDEs) with an autonomous vector field. The introduction of Caputo FDEs in the 1960s allowed initial value problems to be handled more naturally and the asymptotic behaviour of models based on them to be investigated by researchers. More recently, mathematically defined dynamical systems generated by Caputo FDEs and their attractors have been introduced. Dissipative Caputo FDEs have vector fields which satisfy a dissipativity property. For ordinary differential equations (ODEs) it follows from such a property that an absorbing set exists which contains all the long-term dynamical behaviour of the system such as the existence of an attractor. The situation is more complicated for Caputo FDEs, since these are essentially integral equations, and the dissipative inequalities cannot be so easily exploited. Moreover, such integral equations are essentially nonautonomous due to the form of the kernel in the integral equations, even when the vector field is "autonomous," i.e., does not depend explicitly on time. The book is based on recent results of the three coauthors in various combinations with each other and with their other coauthors, in particular Nguyen Dinh Cong and Hieu Trinh. The main aim is to develop and present a theory of dynamical systems and their attractors for Caputo FDEs.
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