This is an introductory-level text on fractional calculus and fractional differential equations. Targeted to graduate students of mathematics and researchers, it contains several new definitions of fractional integrals and fractional derivatives. With interesting applications of the subject in several areas of physical sciences, life sciences, engineering, and technology, the book helps the students understand the importance and developments of this topic. The book is enriched with a list of useful references to published literature, and the presentation of the book is entirely new and easily comprehensible to the students. Some of the topics are refined, and new examples are included to supplement theories to help students understand the concepts easily and clearly.

Autorentext

K. Balachandran, Ph.D., is Mentor Faculty at the Department of Mathematics, Bharathiar University, Coimbatore, Tamil Nadu, India. Earlier, he was Reader (1988-1994), Professor (1994-2016), and finally the Head (2008-2016) of the Department of Mathematics and the UGC-BSR Faculty Fellow (2016-2020) at the same university. Before joining Bharathiar University, he was Lecturer at University of Madras, PG Centre, Salem (1986-1988). He received his Ph.D. degree in Applied Mathematics from the University of Madras, India, in 1985. Prof. Balachandran, Distinguished Scientist, is awarded the Fulbright Visiting Fellowship at the University of Tennessee at Chattanooga, USA, in 1996; the Chandna Mathematics Award in recognition of distinguished and outstanding contributions to mathematics research and teaching in 1999; the Tamil Nadu Scientist Award in 2001; the Global Research Award of the US Navy in 2012; and the UGC-BSR Faculty Fellowship in 2016.

He has participated and delivered invited talks at several national and international conferences, as well as in many universities in India and abroad. Under his supervision, several candidates were awarded Ph.D. degrees in the fields of control theory, differential and integral equations, stochastic differential equations, partial differential equations, mathematical biology, fractional differential equations, and general topology. To his credit, he has published a good number of research papers in these fields and many papers are in SCI journals. He is acting as Referee for various international journals and Associate Editor of some international journals. He is Reviewer for Mathematical Reviews, AMS, and ZbMath. He was Visiting Scientist/Professor at the International Centre for Theoretical Physics, Italy (1987, 1990); University of Tennessee at Chattanooga, USA (1993); Pusan National University, South Korea (1997); University Wyoming, USA (2004); and Naval Postgraduate School, USA (2012); Sophia University, Japan (1998); and Yonsei University, South Korea (2005); and the Pusan National University, South Korea (1999-2000, 2008-2009). He has delivered invited lectures at Yonsei University, South Korea (October 2003), University of Wyoming, USA (June 2004), Hanoi Normal University, Vietnam (June 2011), Sungkyunkwan University, South Korea (December 2011), Kongju National University, South Korea (June 2017), Yangzhou University, China (May 2019) and King Fahd University of Petroleum and Minerals, Saudi Arabia (December 2019). He has participated in the International Congress of Mathematicians and International Congress on Industrial and Applied Mathematics held at Beijing, Madrid, Zurich, Hyderabad, Vancouver, Seoul, Rio de Janeiro and Valencia.