Special Functions in Fractional Calculus and Engineering
暫譯: 分數微積分與工程中的特殊函數

特殊函數在解決各類普通和偏微分方程及其分數階類比中扮演著非常重要的角色，這些方程模型化了現實生活中的情況。由於其非局部性質和記憶效應，分數微積分能夠建模許多在工程中出現的情況。本書包含了一系列與這些方程相關的主題，以及它們在工程中的相關性和重要性。

《分數微積分與工程中的特殊函數》強調了特殊函數在解決具有工程應用的分數階微分方程中的重要性和適用性。本書專注於分數微積分在與工程科學相關的建模中的非局部性質和記憶效應，並涵蓋了使用特殊函數解決與工程科學相關的各類型分數階模型的多種重要且有用的方法。本書進一步通過證明特殊函數在解決分數階微分方程、積分方程和積分微分方程中的廣泛應用和實用性來說明其適用性和價值。

本書涵蓋了多種相互關聯的基礎和進階主題，並具有跨學科的應用，結合了應用數學和工程科學，對於對特殊函數、分數微積分、數學建模和工程感興趣的研究生、博士生、研究人員和教育工作者都非常有用。

Dr. Harendra Singh is an Assistant Professor at the Department of Mathematics, Post-Graduate College, Ghazipur-233001, Uttar Pradesh, India, and has been listed in the top 2% scientists list published by Stanford University. He primarily teaches subjects such as real and complex analysis, functional analysis, abstract algebra, and measure theory in post-graduate level courses in mathematics. Dr. Singh has published 50 research papers in various journals of repute and has published three books from Taylor and Francis, one with Springer and one with Elsevier. He has attained a number of national and international conferences and presented several research papers. He is a reviewer of various journals, and his areas of interest are mathematical modeling, Fractional differential equations, integral equations, calculus of variations, and analytical and numerical methods.

Dr. H. M. Srivastava is a Professor Emeritus, Department of Mathematics and Statistics, University of Victoria, British Columbia V8W 3R4, Canada. He earned his Ph.D. degree in 1965 while he was a full-time member of the teaching faculty at the Jai Narain Vyas University of Jodhpur in India (since 1963). Professor Srivastava has held (and continues to hold) numerous Visiting, Honorary and Chair Professorships at many universities and research institutes in different parts of the world. Having received several D.Sc. degrees as well as honorary memberships and fellowships of many scientific academies and scientific societies around the world, he is also actively associated editorially with numerous international scientific research journals as an Honorary or Advisory Editor or as an Editorial Board Member. He has also edited many special issues of scientific research journals as the Lead or Joint Guest Editor. He has published 36 books, monographs, and edited volumes, 36 books (and encyclopedia) chapters, 48 papers in international conference proceedings, and more than 1350 peer-reviewed international scientific research journal articles, as well as Forewords and Prefaces to many books and journals. Dr. Srivastava's research interests include several areas of pure and applied mathematical sciences, such as real and complex analysis, fractional calculus and its applications, integral equations and transforms, higher transcendental functions and their applications, q-series and q-polynomials, analytic number theory, analytic and geometric inequalities, probability and statistics, and inventory modeling and optimization.

Dr. Rajesh Pandey is an Associate Professor in the Department of Mathematical Sciences, at the Indian Institute of Technology (BHU), Varanasi, India. He is the recipient of the Indo-US fellowship and INSA Visiting Fellowship for the year 2012. He had been a visiting faculty member at the Southern Illinois University, Carbondale Illinois, IL, during 2012-13, The University of Tokyo, Japan from Nov-Dec, 2010, Central South University China, and Shanghai University Shanghai, China in Dec. 2020. He has also worked as an Assistant Professor in Mathematics at BITS Pilani and the Indian Institute of Information Technology Design and Manufacturing Jabalpur from July 2009-May 2014. Dr. Pandey received his Ph.D. degree from the Department of Applied Mathematics, Institute of Technology (BHU), Varanasi, India in 2009 and has published 60 research papers in refereed journals and guided 8 Ph.D. students. He has been a member of management committees for academic institutions and also a member of the advisory committees in various national and international conferences. His current areas of research include fractional derivatives, image processing, and numerical methods for integral and integrodifferential equations.

哈倫德拉·辛格博士（Dr. Harendra Singh）是印度北方邦加齊布爾（Ghazipur-233001）研究生學院數學系的助理教授，並被史丹佛大學列入前2%的科學家名單。他主要教授的課程包括實數與複數分析、泛函分析、抽象代數和測度論等數學研究生課程。辛格博士在多個知名期刊上發表了50篇研究論文，並出版了三本由泰勒與法朗西斯（Taylor and Francis）出版的書籍、一部由施普林格（Springer）出版的書籍，以及一部由愛思唯爾（Elsevier）出版的書籍。他參加了多個國內和國際會議並發表了多篇研究論文。他是多個期刊的審稿人，研究興趣包括數學建模、分數微分方程、積分方程、變分法以及分析和數值方法。

H. M. 斯里瓦斯塔瓦博士（Dr. H. M. Srivastava）是加拿大不列顛哥倫比亞省維多利亞大學數學與統計系的名譽教授。他於1965年獲得博士學位，當時是印度喬德布爾的賈伊·納賴因·維亞斯大學（Jai Narain Vyas University）全職教學成員（自1963年起）。斯里瓦斯塔瓦教授在世界各地的多所大學和研究機構擔任（並持續擔任）多個訪問、名譽及講座教授職位。他獲得了多個D.Sc.學位以及世界各地多個科學學會和科學社團的名譽會員和研究員資格，並且作為名譽或顧問編輯或編輯委員會成員，積極參與多個國際科學研究期刊的編輯工作。他還作為主編或聯合客座編輯編輯了多個科學研究期刊的特刊。他出版了36本書籍、專著和編輯卷，36篇書籍（和百科全書）章節，48篇國際會議論文，以及超過1350篇經過同行評審的國際科學研究期刊文章，還有多本書籍和期刊的前言和序言。斯里瓦斯塔瓦博士的研究興趣包括純數學和應用數學科學的多個領域，如實數與複數分析、分數微積分及其應用、積分方程和變換、高等超越函數及其應用、q級數和q多項式、解析數論、解析和幾何不等式、概率與統計，以及庫存建模和優化。

拉傑什·潘德博士（Dr. Rajesh Pandey）是印度瓦拉納西印度理工學院（Indian Institute of Technology (BHU)）數學科學系的副教授。他是2012年印美獎學金和印度科學院訪問獎學金的獲得者。他曾於2012至2013年在南伊利諾伊大學（Southern Illinois University, Carbondale Illinois, IL）擔任訪問教員，於2010年11月至12月在日本東京大學（The University of Tokyo）任教，並於2020年12月在中國中南大學（Central South University）和上海大學（Shanghai University）任教。他還曾於2009年7月至2014年5月在比特斯·皮拉尼（BITS Pilani）和印度信息技術設計與製造學院（Indian Institute of Information Technology Design and Manufacturing Jabalpur）擔任數學助理教授。潘德博士於2009年在印度瓦拉納西技術學院（Institute of Technology (BHU)）應用數學系獲得博士學位，並在同行評審期刊上發表了60篇研究論文，指導了8名博士生。他曾是學術機構管理委員會的成員，並在各種國內和國際會議中擔任顧問委員會成員。他目前的研究領域包括分數導數、影像處理以及積分和積分微分方程的數值方法。