Based on the fractional calculus theory, numerical calculation theory and machine learning, fractional calculus team established mathematical models of complex media, developed new numerical algorithms and theories based on fractional operators, and applied them to fluid mechanics, quantum mechanics, etc. In recent years, the team has systematically established the theoretical framework of fractional calculus and studied the mechanical mechanism of anomalous  phenomena in mass transport, energy diffusion and momentum transfer. A series of innovative achievements have been made in the field of complex medium fractional equation modeling, analytical and numerical calculation, parameter identification and so on. The achievement was awarded one second prize of natural science of Shandong Province.

      Xiaoyun jJiang, Leader of the National Ten Thousand Talents Program， doctoral supervisor, National May 1 female pacesetter and member of the national non-Newtonian fluid mechanics Professional Committee. She is mainly engaged in the research of fractional calculus theory and applications, non-Newtonian fluid mechanics and other fields. She has made a series of innovative achievements in the fields of complex medium modeling, analytical and numerical calculation, parameter identification, etc., and has solved many difficult problems in modeling and calculation in anomalous transport process.The researchwas awarded one second prize of natural science of Shandong Province (the first one). She has presided over one major research plan / cultivation project of National Natural Science Foundation of China. She has presided over three general projects of National Natural Science Foundation of China. She has published more than 60 SCI papers and SCI cited more than 700 times. Her achievements have been highly appraised and widely cited by experts in various fields at home and abroad. The results have been published in international top SCI journals such as SIAM Journal on Numerical Analysis, Applied Mathematical Modeling, Journal of Scientific Computing, etc. Over the past five years, a number of graduate students have won awards and honors, such as Outstanding Graduates of Shandong Province, National Scholarship, May Fourth Youth Science Award, President Scholarship of Shandong University, and Pan Chengdong Scholarship. Seven doctoral students graduated in recent five years have successively worked in Shandong University, Southwest University of Finance and economics, Jiangnan University, and entered Shandong University and Chinese Academy of Sciences as postdoctoral students. Four of them were promoted to associate professors after their entry. Due to her outstanding achievements in graduate education, Jiang Xiaoyun was awarded the honorary title of "good tutor in my mind" in the 11th Shandong University.

      Fanhai Zeng is an outstanding young and middle-aged scholar and doctoral supervisor of Shandong University. He has been engaged in the research on the theory and application of fractional calculus, and has made a series of innovative achievements in the fields of modeling, calculation and application of fractional calculus. Professor  Fanhai Zeng has successively engaged in postdoctoral research in the Department of Applied Mathematics of Brown University, the Department of Applied Mathematics of Queensland University of science and technology in Australia and the Department of mathematics of National University of Singapore. So far, he has published 28 SCI papers.  16 papers have been published in the top journals of Computational Mathematics and applied mathematics, Siam J. numeral. Siam J. SCI. Compute, J. SCI. Comput., compute. Methods appl. Mech. Engrg. And J. comput. Phys. They jointly published a monograph in 2015 and won the Shanghai Youxiu doctoral dissertation award in 2016. Professor Fanhai Zeng's papers have been cited more than 800 times in SCI, and the highest number of citations for a single paper has reached more than 170 times. Six papers have been selected as highly cited papers of ESI (as of July 2020), and their achievements have been cited and positively evaluated by well-known scholars at home and abroad. At present, the research fields include spectral method and its application, fractional calculus theory, numerical algorithm and its application, as well as the theory and application of stochastic model and machine learning.

      Hui Zhang , a PhD graduate of Applied Mathematics, majored in Applied Mathematics from September 2014 to June 2019, studied under Professor Xiaoyun Jiang, and is now a postdoctoral student in special funded program of Shandong University. Up to now, 17 SCI papers have been published in the Journal of computational physics and other authoritative computing journals, including 12 first authors or corresponding authors. She was supported by the National Postdoctoral innovation talent support program in 2019 and the national doctoral foundation. He has visited Queensland University of science and technology in Australia and Nanyang Polytechnic University in Singapore. During the University, she has won the President Scholarship of Shandong University, national scholarship for graduate students, outstanding students of Shandong Province, outstanding graduates of Shandong Province, the 10th "May 4th" Youth Science Award of Shandong University, and two outstanding academic achievement awards of Shandong University.