Boundary Value Problems: Essential Fractional Dynamic Equations on Time Scales

Georgiev, Svetlin

Boundary Value Problems: Essential Fractional Dynamic Equations on Time Scales
  • 出版商: Springer
  • 出版日期: 2024-08-18
  • 售價: $1,840
  • 貴賓價: 9.5 折 $1,748
  • 語言: 英文
  • 頁數: 163
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303138198X
  • ISBN-13: 9783031381980

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相關主題

商品描述

This book explores boundary value problems for Riemann-Liouville fractional dynamic equations on arbitrary time scales as well as the shifting problem on the whole time scale. The author includes an introductory overview of fractional dynamic calculus on time scales. The book also introduces the Laplace transform on arbitrary time scales, including the bilateral Laplace transform, the Laplace transform of power series, and a deduction of an inverse formula. The author then discusses the generalized convolutions of functions on arbitrary time scales and the shifting problem for existence of solutions. The book moves on to cover boundary value problems and initial boundary value problems for some classes Riemann-Liouville fractional dynamic equations.
In addition, this book:
  • Explains the topic for a wide audience including physicists, engineers, biologists, and students of various disciplines
  • Presents a solution technique applicable to other problems for fractional dynamic equations on arbitrary time scales
  • Provides an introduction to boundary value problems for fractional dynamic equations on arbitrary time scales

商品描述(中文翻譯)

本書探討了在任意時間尺度上 Riemann-Liouville 分數動態方程的邊界值問題，以及整個時間尺度上的位移問題。作者包含了分數動態微積分在時間尺度上的簡介概述。本書還介紹了在任意時間尺度上的拉普拉斯變換，包括雙邊拉普拉斯變換、冪級數的拉普拉斯變換，以及逆公式的推導。接著，作者討論了在任意時間尺度上函數的廣義卷積及其解的存在性位移問題。本書進一步涵蓋了某些類別的 Riemann-Liouville 分數動態方程的邊界值問題和初始邊界值問題。

此外，本書：
- 為包括物理學家、工程師、生物學家及各學科學生在內的廣泛讀者解釋了該主題
- 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決技術
- 提供了分數動態方程在任意時間尺度上邊界值問題的介紹

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式》、《模糊動態方程式》、《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式》，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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