Special Functions and Analysis of Differential Equations
暫譯: 特殊函數與微分方程的分析

Agarwal, Praveen, Agarwal, Ravi P., Ruzhansky, Michael

Special Functions and Analysis of Differential Equations
  • 出版商: CRC
  • 出版日期: 2020-09-09
  • 售價: $6,820
  • 貴賓價: 9.5 折 $6,479
  • 語言: 英文
  • 頁數: 370
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 0367334720
  • ISBN-13: 9780367334727

    • 海外代購書籍(需單獨結帳)

商品描述

Differential Equations are very important tool in Mathematical Analysis. These are widely found in mathematics itself and in its applications to Statistics, computing, electrical circuit analysis, dynamical systems, economics, biology and so on. Recently there has been an increasing interest in and widely extended use of differential equations and systems of fractional order (that is, of arbitrary order), as better models of phenomena of various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations.

This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and PDE's problems. Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDE's, and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.

Specific topics include but are not limited to:

  • Partial differential equations

  • Least-squares on First-Order system

  • Sequence and series in functional analysis

  • Special functions related to fractional (non-integer) order control systems and equations

  • Various special functions related to generalized fractional calculus

  • Operational method in fractional calculus

  • Functional analysis and operator theory

  • Mathematical physics

  • Applications of numerical analysis and applied mathematics

  • Computational mathematics

  • Mathematical modeling

This book provide the recent developments in Special functions and Differential Equations and publishing high quality peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations and related applications.

商品描述(中文翻譯)

微分方程在數學分析中是一個非常重要的工具。這些方程在數學本身及其在統計學、計算、電路分析、動態系統、經濟學、生物學等應用中廣泛存在。最近，對微分方程和分數階系統（即任意階數）的興趣日益增加，這些方程作為各種物理、工程、自動化、生物學和生醫學、化學、地球科學、經濟學、自然等現象的更好模型而被廣泛應用。現在，與分數微積分相關的特殊函數的新統一呈現和廣泛發展是必要的工具，這些工具與任意階數的微分和積分理論（即分數微積分）以及分數階（或多階）微分和積分方程有關。

本書為學習者提供了發展對特殊函數進展的理解以及應用先進數學技術解決複雜微分方程和偏微分方程問題所需技能的機會。主題應與涉及數學分析及其眾多應用的特殊函數密切相關。本書的主要目標是強調複分析理論中基本結果和技術對微分方程和偏微分方程的重要性，並強調專門針對物理、化學、生物學和工程中出現的問題的數學處理的文章，特別是那些強調分析方面和新問題及其解決方案的文章。

具體主題包括但不限於：

- 偏微分方程
- 一階系統的最小二乘法
- 功能分析中的序列和級數
- 與分數（非整數）階控制系統和方程相關的特殊函數
- 與廣義分數微積分相關的各種特殊函數
- 分數微積分中的運算方法
- 功能分析和算子理論
- 數學物理
- 數值分析和應用數學的應用
- 計算數學
- 數學建模

本書提供了特殊函數和微分方程的最新發展，並在非線性分析、常微分方程、偏微分方程及相關應用領域出版高質量的同行評審書章。

作者簡介

Praveen Agarwal is Professor at the Department of Mathematics, Anand International College of Engineering, Jaipur, India. On the editorial boards of several journals of repute and conducted, Professor Agarwal has conducted and attended a number of conferences. Recently, he has received the Most Outstanding Researcher 2018 award for his contribution to mathematics by the Union Minister of Human Resource Development of India. He has received numerous international research grants. He has published over 250 articles related to special functions, fractional calculus and mathematical physics in several leading mathematics journals. His latest research has focused on partial differential equations, fixed point theory and fractional differential equations.

Ravi P. Agarwal received his Ph.D. in mathematics from the Indian Institute of Technology, Madras, India. He is a professor of mathematics at the Florida Institute of Technology. His research interests include numerical analysis, inequalities, fixed point theorems, and differential and difference equations. He is the author/co-author of over 1000 journal articles and more than 25 books, and actively contributes to over 500 journals and book series in various capacities.

Michael Ruzhansky is a professor at the Department of Mathematics, Imperial College London. He has published over 100 research articles in several leading international journals. He has also published five books and memoirs and nine edited volumes. He has researched topics related to pseudo-differential operators, harmonic analysis and partial differential equations. More recently, he has worked on boundary value problems and their applications. He has been on the editorial board of many respected international journals and served as the President of the International Society of Analysis, Applications, and Computations (ISAAC) in the period 2009-2013.

作者簡介(中文翻譯)

Praveen Agarwal 是印度齋浦爾安納德國際工程學院數學系的教授。他在多個知名期刊的編輯委員會任職，並參加和舉辦了多場會議。最近，他因對數學的貢獻獲得了印度人力資源發展部部長頒發的2018年最傑出研究者獎。他獲得了多項國際研究補助金，並在多本領先的數學期刊上發表了超過250篇與特殊函數、分數微積分和數學物理相關的文章。他最新的研究集中在偏微分方程、固定點理論和分數微分方程上。

Ravi P. Agarwal 於印度馬德拉斯印度理工學院獲得數學博士學位。他是佛羅里達理工學院的數學教授。他的研究興趣包括數值分析、不等式、固定點定理以及微分方程和差分方程。他是超過1000篇期刊文章和25本以上書籍的作者或合著者，並以各種身份積極貢獻於超過500本期刊和書系。

Michael Ruzhansky 是倫敦帝國學院數學系的教授。他在多個領先的國際期刊上發表了超過100篇研究文章。他還出版了五本書籍和回憶錄，以及九本編輯卷。他的研究主題涉及偽微分算子、調和分析和偏微分方程。最近，他專注於邊值問題及其應用。他曾在多個受尊敬的國際期刊的編輯委員會任職，並於2009年至2013年期間擔任國際分析、應用與計算學會（ISAAC）的會長。

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