Attractors of Caputo Fractional Differential Equations / by Thai Son Doan, Peter E. Kloeden, Hoang The Tuan.

Format:

Book

Author/Creator:

Doan, Thai Son.

Contributor:

Kloeden, Peter E.

Tuan, Hoang The.

Series:

SpringerBriefs in Mathematics, 2191-8201

Language:

English

Subjects (All):

Differential equations.

Dynamics.

Differential Equations.

Dynamical Systems.

Local Subjects:

Differential Equations.

Dynamical Systems.

Physical Description:

1 online resource (233 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

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.

Contents:

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.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-032-05511-3

9783032055118

OCLC:

1572190468