Pablo Raúl Stinga, Associate Professor of Mathematics, has published the featured article “Fractional Derivatives: Fourier, Elephants, Memory Effects, Viscoelastic Materials, and Anomalous Diffusions” that appears in the April 2023 issue of the monthly magazine Notices of the American Mathematical Society.
The Notices is the world’s most widely read magazine aimed at professional mathematicians. As the magazine of record for the American Mathematical Society, Notices publicizes activities of the Society and provides opportunities for mathematicians and students of mathematics to find out what is going on in their field. Each issue of Notices contains high-level expository articles written by STEM professionals in industry and academia.
Stinga’s article introduces the reader to the fascinating world of fractional calculus. This area began when Leibniz, one of the founders of calculus, asked the question “what is the derivative of fractional order of a function?” The article gives a brief historical account, considering the crucial roles played by Leibniz and Fourier. Recent advances on the modern theory of fractional calculus are presented. In addition, Stinga addresses some controversial questions and concerns that have been raised by some in the scientific community. Finally, three different applications of fractional calculus to real-world phenomena are explained: how to predict the growth of the world population by factoring in memory effects; how to model the response of viscoelastic materials such as asphalt, wood or skin tissue; and how to capture the phenomenon of anomalous diffusion observed in the way monkeys travel and plasmas particles move.
The article is accessible to undergraduate students familiar with calculus.