Special Functions in Fractional Calculus and Engineering

Special functions play a very important role in solving various families of ordinary and partial differential equations as well as their fractional-order analogs which model real-life situations. Due to the non-local nature and memory effect, fractional calculus is capable of modeling many situations which arise in engineering. This book includes a collection of related topics associated with such equations and their relevance and significance in engineering.

Special Functions in Fractional Calculus and Engineering highlights the significance and applicability of special functions in solving fractional-order differential equations with engineering applications. The book focuses on the non-local nature and memory effect of fractional calculus in modeling relevant to engineering science and covers a variety of important and useful methods using special functions for solving various types of fractional-order models relevant to engineering science. The book goes on to illustrate the applicability and usefulness of special functions by justifying their numerous and widespread occurrences in the solution of fractional-order differential, integral, and integrodifferential equations.

The book holds a wide variety of interconnected fundamental and advanced topics with interdisciplinary applications that combine applied mathematics and engineering sciences. useful to graduate students, Ph.D. scholars, researchers, and educators interested in special functions, fractional calculus, mathematical modeling, and engineering.

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特殊函數在解決各種普通和偏微分方程以及其分數階模型（模擬現實情況）中扮演著非常重要的角色。由於分數微積分的非局部性和記憶效應，它能夠模擬工程中出現的許多情況。本書包含了與這些方程及其在工程中的相關性和重要性相關的主題集合。《分數微積分和工程中的特殊函數》突出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應用性。本書著重介紹了分數微積分的非局部性和記憶效應在與工程科學相關的建模中的應用，並介紹了使用特殊函數解決各種與工程科學相關的分數階模型的重要且有用的方法。本書還通過證明特殊函數在解決分數階微分、積分和積分微分方程中的廣泛應用和有用性。本書涵蓋了一系列相互關聯的基礎和高級主題，並結合了應用數學和工程科學，對對特殊函數、分數微積分、數學建模和工程感興趣的研究生、博士研究生、研究人員和教育工作者非常有用。

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.

Dr. Harendra Singh是印度北方邦Ghazipur-233001的Post-Graduate College數學系的助理教授，並被斯坦福大學列為前2%的科學家名單。他主要在研究生數學課程中教授實分析、復分析、泛函分析、抽象代數和測度論等科目。Dr. Singh在多個知名期刊上發表了50篇研究論文，並出版了三本由Taylor and Francis出版社、一本由Springer出版社和一本由Elsevier出版社出版的書籍。他參加了多個國內外會議並發表了多篇研究論文。他是多個期刊的審稿人，他的研究興趣包括數學建模、分數微分方程、積分方程、變分計算以及分析和數值方法。

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學系的名譽教授。他在1965年獲得博士學位，當時他是印度Jodhpur的Jai Narain Vyas大學的全職教學人員（自1963年起）。Srivastava教授在世界各地的許多大學和研究機構擔任過（並繼續擔任）訪問、榮譽和講座教授職位。他獲得了多個D.Sc.學位，並成為世界各地許多科學院和科學學會的榮譽會員和會士，他還在許多國際科學研究期刊上擔任榮譽或諮詢編輯或編輯委員會成員。他還編輯了許多科學研究期刊的特刊，擔任首席或聯合客座編輯。他出版了36本書籍、專著和編輯的專輯，36本（和百科全書）章節，48篇國際會議論文，以及超過1350篇同行評審的國際科學研究期刊文章，還有許多書籍和期刊的前言和序言。Srivastava博士的研究興趣包括純粹和應用數學科學的多個領域，如實分析、復分析、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-數列和q-多項式、解析數論、解析和幾何不等式、概率和統計以及庫存建模和優化。

Dr. Rajesh Pandey是印度Varanasi的印度理工學院（BHU）數學科學系的副教授。他是2012年的印美研究員和INSA訪問研究員的獲獎者。他曾在2012-13年期間擔任美國伊利諾伊州卡本代爾南部伊利諾伊大學的訪問教師，2010年11月至12月在日本東京大學，2020年12月在中南大學和上海大學中國擔任訪問教師。他還曾在2009年7月至2014年5月期間擔任比特斯比拉尼和印度信息技術設計和製造賈巴爾普爾印度理工學院的數學助理教授。Pandey博士於2009年在印度Varanasi的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。他曾擔任學術機構的管理委員會成員，並擔任多個國內外會議的諮詢委員會成員。他目前的研究領域包括分數導數、圖像處理以及積分和積分微分方程的數值方法。