Fractional Differential Equations: An Approach Via Fractional Derivatives

This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

這本研究生教科書提供了一個自成一體的介紹，關於現代分數微分方程的數學理論。它涵蓋了普通和偏微分方程，並著重於詳細的解決方案理論，特別是在對問題數據進行現實假設的情況下的正則性理論。本書包含了廣泛的參考文獻、應用驅動的建模、大量的練習題和圖形插圖，以補充其對該領域的全面介紹。它建議給應用和計算數學的研究生和研究人員閱讀，特別是應用分析、數值分析和反問題領域的研究者。

Bangti Jin received the B.Eng. degree in polymeric materials and engineering in 2002, theM.Sc. degree in computational mathematics in 2005, both from Zhejiang University, Hangzhou, China, and the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was an Assistant Professor of mathematics at the University of California, Riverside (2013-2014), a Visiting Assistant Professor at Texas A&M University (2010-2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009-2010). He is currently Professor of Inverse Problems at the Department of Computer Science, University College London, London, U.K. His research interests include computational inverse problems and numerical analysis of differential equations.

Bangti Jin於2002年獲得浙江大學高分子材料與工程學士學位，2005年獲得計算數學碩士學位，並於2008年在香港中文大學獲得應用數學博士學位。在此之前，他曾任職於加州大學河濱分校數學助理教授（2013-2014年），德克薩斯A＆M大學訪問助理教授（2010-2013年），以及不來梅大學亞歷山大·馮·洪堡博士後研究員（2009-2010年）。他目前是倫敦大學學院計算機科學系的反問題教授。他的研究興趣包括計算反問題和微分方程的數值分析。