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College of Liberal Arts and Sciences | Mathematics

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February 4, 2019 | 2:45 p.m. - 4:00 p.m.
Category: Lecture
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Pablo R. Stinga, Iowa State University

Title: What is a fractional derivative?

Abstract:

Fractional derivatives and integrals are effective tools to model anomalous diffusions in plasmas, population migration and electrical signal propagation in cardiac tissue. Abel was the first one to use fractional integrals in 1823 to solve the tautochrone problem. Several definitions of fractional derivatives are named after Riemann, Liouville, Caputo, Marchaud and many others. We will give a quick overview on some of these popular definitions. We will also introduce the Mitagg-Leffler functions, which in this context are the fractional analogues to the usual exponential functions. Then we will show a unified approach to fractional derivatives based on the use of semigroups. This will make evident the one-sided nature of fractional derivatives. In the end we will present a (one-sided) Fundamental Theorem of the Fractional Calculus and a characterization of (one-sided) fractional Sobolev spaces.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.