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Prof. Fanhai ZENG
School of Mathematics
Shandong University


We develop two fast memory saving methods for calculating the fractional integral and derivative operators.
Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity for dealing with the fractional derivative operator. Our fast method simplifies the existing one [SIAM J. Sci. Comput., 28 (2006), pp. 421–438].


Prof. Fanhai ZENG received his bachelor degree from Northwestern Polytechnical University in 2005. In 2014, he graduated from Shanghai University with a Ph.D. degree. His research interest is in computational mathematics and fractional differential equations. He works as a Professor at Shandong University.
From 2014 to 2020, he did post-doctoral research at Brown University in the United States, Queensland University of Technology in Australia and the National University of Singapore. He co-published a monograph in 2015, won the Shanghai Excellent Doctoral Dissertation Award in 2016, published more than 30 papers in international journals such as SINUM, SISC, JSC, JCP and CMAME, and was cited by SCIE more than 1,000 times.


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