Attractors of Caputo Fractional Differential Equations
暫譯: 卡普托分數微分方程的吸引子

Doan, Thai Son, Kloeden, Peter E., Tuan, Hoang The

Attractors of Caputo Fractional Differential Equations
  • 出版商: Springer
  • 出版日期: 2026-01-03
  • 售價: $2,470
  • 貴賓價: 9.5 折 $2,347
  • 語言: 英文
  • 頁數: 140
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3032055105
  • ISBN-13: 9783032055101
  • 相關分類: 微積分 Calculus

    • 海外代購書籍(需單獨結帳)

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商品描述

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.

商品描述(中文翻譯)

本書專注於具有自主向量場的耗散型 Caputo 分數微分方程 (FDEs)。在1960年代引入的 Caputo FDEs 使得初始值問題的處理變得更加自然，並且研究人員能夠探討基於這些方程的模型的漸近行為。最近，數學上定義的由 Caputo FDEs 生成的動態系統及其吸引子也被引入。

耗散型 Caputo FDEs 具有滿足耗散性質的向量場。對於常微分方程 (ODEs) 而言，這樣的性質意味著存在一個吸收集，該集合包含系統的所有長期動態行為，例如吸引子的存在。對於 Caputo FDEs 情況則更為複雜，因為這些方程本質上是積分方程，且耗散不等式無法如此輕易地利用。此外，這些積分方程本質上是非自主的，因為積分方程中的核的形式，即使向量場是「自主的」，即不明確依賴於時間。

本書基於三位共同作者最近的研究成果，這些成果是他們之間以及與其他共同作者（特別是 Nguyen Dinh Cong 和 Hieu Trinh）之間的各種組合。主要目的是為 Caputo FDEs 發展和呈現動態系統及其吸引子的理論。

作者簡介

Peter E. Kloeden is retired Chair of Applied and Instrumental Mathematics is the Goethe University Frankfurt and is now a visiting researcher at the University of Tübingen. His research interests include analysis and numerics of random and nonautonomous systems and their applications. He is a Fellow of SIAM and was awarded the W. T. and Idalia Reid Prizefrom SIAM in 2006. In 2014, he received a Thousand Talents Award from the government of China. He served as co-editor-in-chief of Discrete and Continuous Dynamical Systems, Series B. He is the co-author of best selling books on stochastic numerics, numerical dynamics, nonautonomous dynamical systems, lattice systems, fuzzy metric spaces, etc.

作者簡介(中文翻譯)

彼得·E·克勞登（Peter E. Kloeden）是法蘭克福歌德大學應用與儀器數學的退休主席，目前擔任圖賓根大學的訪問研究員。他的研究興趣包括隨機與非自治系統的分析與數值方法及其應用。他是美國工業與應用數學學會（SIAM）的會士，並於2006年獲得SIAM頒發的W. T.和Idalia Reid獎。2014年，他獲得中國政府的千人計畫獎。他曾擔任《離散與連續動態系統，B系列》的共同主編。他是多本暢銷書的共同作者，內容涵蓋隨機數值方法、數值動力學、非自治動態系統、格子系統、模糊度量空間等。

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