Department of

December 2015 January 2016 February 2016 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 3 4 5 6 6 7 8 9 10 11 12 3 4 5 6 7 8 9 7 8 9 10 11 12 13 13 14 15 16 17 18 19 10 11 12 13 14 15 16 14 15 16 17 18 19 20 20 21 22 23 24 25 26 17 18 19 20 21 22 23 21 22 23 24 25 26 27 27 28 29 30 31 24 25 26 27 28 29 30 28 29 31

Wednesday, January 27, 2016

**Abstract:** The concept of fractional derivatives was introduced almost at the same time that the concept of integer order derivatives was introduced. In recent years, the concept and applications of fractional derivatives have received considerable interest in almost every area of science, engineering, applied mathematics, bioengineering and economics. It has been demonstrated that fractional derivatives based models provide more accurate models of many systems than their integer order models do. In this talk, I will introduce several definitions of fractional derivatives used in the literature. I will demonstrate that integer order derivatives are defined using local information. In contrast, past history of a system is needed to define a fractional derivative. As a result, fractional derivatives turn out to be useful in modeling systems with memory. I will discuss several applications where fractional derivatives arise. These applications include tautochrone problem, modeling of a disk brake, viscoelastic system, lossy transmission line and lossy capacitor, and vibration of a plate submerged in a fluid. I will compare experimental and analytical results where possible. Many researchers avoid models containing fractional derivatives because they assume that these models require a strong theoretical background in fractional calculus. In this talk, I will demonstrate that tools can be developed to hide mathematical details necessary to solve equations involving fractional derivatives. I will also demonstrate applications of these tools in solving fractional differential equations and fractional control problems. Finally, I will mention the areas where fractional derivatives are being applied today. Although considerable research has been done on applications of fractional derivatives, much remains to be done. It is my hope that this presentation will encourage you to start doing research in the area of fractional derivatives. Lunch will be provided.