Boundary Value Problems: Advanced Fractional Dynamic Equations on Time Scales

Georgiev, Svetlin

Boundary Value Problems: Advanced Fractional Dynamic Equations on Time Scales
  • 出版商: Springer
  • 出版日期: 2024-08-18
  • 售價: $1,820
  • 貴賓價: 9.5 折 $1,729
  • 語言: 英文
  • 頁數: 147
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031382021
  • ISBN-13: 9783031382024

    • 海外代購書籍(需單獨結帳)

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商品描述

This book explores boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. The author provides an introduction to each fractional dynamic equation before delving into the problems. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions.
In addition, this book:
  • Explains the topic for a wide audience including physicists, engineers, biologists, and students of various disciplines
  • Explores boundary value problems for advanced fractional dynamic equations on arbitrary time scales
  • Presents a solution technique applicable to other problems for fractional dynamic equations on arbitrary time scales
About the Author:
Svetlin Georgiev, Ph.D., is an Assistant Professor in the Faculty of Mathematics and Informatics at Sofia University. He was previously affiliated with Sorbonne University. He is the author of several books, including Real Quaternion Calculus Handbook, Theory of Distributions, Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales, and Functional Dynamic Equations on Time Scales, published by Springer Nature. His current research interests include harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.

商品描述(中文翻譯)

本書探討了在任意時間尺度上分數動態方程的邊界值問題，包括 Caputo 分數動態方程、衝擊性 Caputo 分數動態方程和衝擊性 Riemann-Liouville 分數動態方程。作者在深入問題之前，對每種分數動態方程進行了介紹。本書還涵蓋了每種類型方程的初始值問題、邊界值問題和初始邊界值問題。作者提供了解的積分表示，並證明了解的存在性和唯一性。

此外，本書：
- 為廣泛的讀者群體解釋了該主題，包括物理學家、工程師、生物學家以及各學科的學生
- 探討了在任意時間尺度上高級分數動態方程的邊界值問題
- 提出了適用於其他任意時間尺度上分數動態方程問題的解法技術

關於作者：
Svetlin Georgiev 博士是索非亞大學數學與資訊學院的助理教授。他曾在索邦大學任職。他是幾本書的作者，包括《實四元數微積分手冊》、《分佈理論》、《時間尺度上的分數動態微積分與分數動態方程》、《模糊動態方程》、《時間尺度上的動態包含與最優控制問題》和《時間尺度上的函數動態方程》，這些書籍均由 Springer Nature 出版。他目前的研究興趣包括調和分析、函數分析、偏微分方程、常微分方程、Clifford 和四元數分析、積分方程以及時間尺度上的動態微積分。

作者簡介

Svetlin G. Georgiev, Ph.D., is an Assistant Professor in the Faculty of Mathematics and Informatics at Sofia University. He was previously affiliated with Sorbonne University. He is the author of several books, including Real Quaternion Calculus Handbook, Theory of Distributions, Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales, Fuzzy Dynamic Equations, Dynamic Inclusions and Optimal Control Problems on Time Scales, and Functional Dynamic Equations on Time Scales, published by Springer Nature. His current research interests include harmonic analysis, functional analysis, partial differential equations, ordinary differential equations, Clifford and quaternion analysis, integral equations, and dynamic calculus on time scales.

作者簡介(中文翻譯)

Svetlin G. Georgiev, Ph.D.，是索非亞大學數學與資訊學院的助理教授。他之前曾在索邦大學任職。他是幾本書的作者，包括《實四元數微積分手冊》、《分佈理論》、《分數動態微積分與時間尺度上的分數動態方程》、《模糊動態方程》、《時間尺度上的動態包含與最佳控制問題》以及《時間尺度上的函數動態方程》，這些書籍均由Springer Nature出版。他目前的研究興趣包括調和分析、函數分析、偏微分方程、常微分方程、Clifford與四元數分析、積分方程以及時間尺度上的動態微積分。

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