Numerical Methods for Fractal-Fractional Differential Equations and Engineering: Simulations and Modeling
暫譯: 分形-分數微分方程與工程的數值方法：模擬與建模

這本書探討在分形-分數運算子框架下新型混沌系統的模擬與建模。這是第一本提供使用多種分形-分數運算子進行混沌問題的數學建模與模擬的書籍，以尋找解決方案。

Muhammad Altaf Khan completed his master's degree in Applied mathematics from the Kohat University of Science in Technology in 2008. He completed his MS degree from Islamia college University Peshawar in 2012 in Applied mathematics and his research area is Mathematical Biology. He did his Ph.D. in Applied mathematics from Abdul Wali Khan University Mardan in 2015. He served as Lecturer in Abdul Wali Khan Mardan in the Department of Mathematics from 2015-2016 under the Umbrella of faculty development program. After that, he joined the City University of Science and Information Technology Peshawar and served there as Assistant Professor for the period August 2017-September 2019. He joined the post-doctorate position on October 01, 2019-December 2021 at the University of the Free State of South Africa. He also worked as a Researcher at Ton Duc Thang University Vietnam, March 2020-February 2021. He has been an Adjunct Professor at Airlangga University Indonesia for the period March 2021-Till February 2022. He is currently a Research Fellow at the University of the Free State of South Africa. He organized many special issues in reputable ISI journals, such as Advances in Difference equations, Results in Physics, Fractals, Alexandria Engineering Journals, Symmetry MDPI, etc. He is the author of more than 250 publications. He is an active editor in some reputable journals. He is an active researcher and worked working in fractional differential equations, evolutionary differential equations, optimal control problems, infectious diseases modeling, social sciences problems modeling, etc. He is a reviewer for many international journals of Springer, Wily, Hindawi, Elsevier, etc.

Abdon Atangana works at the Institute for Groundwater Studies, University of the Free State, Bloemfontein, South Africa as a Full Professor. His research interests are, but are not limited to, fractional calculus and applications, numerical and analytical methods, and modeling. He is the author of more than 270 research papers and five books in top-tier journals of applied mathematics and groundwater modeling. He is the founder of numerous mathematical operators, for example, fractional differential and integral operators with singular and nonlocal kernels (Atangana-Baleanu derivatives and integral), fractal-fractional calculus, and piecewise calculus, and some numerical methods. He serves as an editor in top-tier journals in various fields of study. He has been invited as a plenary, and keynote speaker at more than 30 international conferences. He was elected Highly Cited Mathematician in 2019, Highly Cited Mathematician with Crossfield Impact in 2020, and Highly Cited Mathematician in 2021. He is a recipient of the Obada price 2020, the TWAS-Hamdan Award 2020, and many others. He is a fellow of the World Academia of Science.

穆罕默德·阿爾塔夫·汗（Muhammad Altaf Khan）於2008年在科哈特科技大學（Kohat University of Science and Technology）獲得應用數學碩士學位。他於2012年在伊斯蘭學院大學（Islamia College University Peshawar）獲得應用數學碩士學位，研究領域為數學生物學。他於2015年在阿卜杜勒·瓦利·汗大學（Abdul Wali Khan University Mardan）獲得應用數學博士學位。2015年至2016年，他在阿卜杜勒·瓦利·汗大學數學系擔任講師，參與教師發展計畫。之後，他加入了城市科技與資訊大學（City University of Science and Information Technology Peshawar），並於2017年8月至2019年9月擔任助理教授。他於2019年10月1日至2021年12月在南非自由州大學（University of the Free State of South Africa）擔任博士後研究員。他還於2020年3月至2021年2月在越南董德湯大學（Ton Duc Thang University Vietnam）擔任研究員。他於2021年3月至2022年2月擔任印尼艾爾朗加大學（Airlangga University）的兼任教授。目前，他是南非自由州大學的研究員。他在多個知名的ISI期刊上組織了許多特刊，如《差分方程的進展》（Advances in Difference Equations）、《物理學結果》（Results in Physics）、《分形》（Fractals）、《亞歷山大工程期刊》（Alexandria Engineering Journals）、《對稱MDPI》（Symmetry MDPI）等。他是超過250篇出版物的作者，並在一些知名期刊擔任活躍編輯。他是一位活躍的研究者，專注於分數微分方程、演化微分方程、最優控制問題、傳染病建模、社會科學問題建模等。他是多本國際期刊的審稿人，包括Springer、Wiley、Hindawi、Elsevier等。

阿布頓·阿坦加納（Abdon Atangana）在南非自由州大學（University of the Free State）地下水研究所（Institute for Groundwater Studies）擔任全職教授。他的研究興趣包括但不限於分數微積分及其應用、數值和解析方法以及建模。他在應用數學和地下水建模的頂級期刊上發表了超過270篇研究論文和五本書籍。他是多個數學運算子的創始人，例如具有奇異和非局部核的分數微分和積分運算子（Atangana-Baleanu導數和積分）、分形-分數微積分和分段微積分，以及一些數值方法。他在各個研究領域的頂級期刊擔任編輯。他曾受邀在超過30個國際會議上擔任全體會議和主題演講者。他於2019年被選為高被引數學家，2020年獲得跨領域影響的高被引數學家，2021年再次被選為高被引數學家。他是2020年Obada獎、2020年TWAS-Hamdan獎及其他多個獎項的獲得者。他是世界科學學院的成員。