Fractional Calculus
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Fractional Calculus
In fractional calculus (FC) we study derivatives of general orders, not necessarily positive integer orders. Thus, it is o.k. to talk about a derivative of order 1/2 or 1/3 depending on the need.
Fractional integral is an integral of arbitrary order, while fractional derivative is a derivative of arbitrary order.
Fractional integrals and derivatives occur naturally in certain modelling problems, such as surface-volume reactions, viscoelasticity, Fourier transform, modelling under friction, turbulence modelling, combinatorics and chaotic dynamics, to name a few.
Fractional calculus research has been a very active and promising research area due to its applications.
Fractional Derivative Seminar at University of Delaware
Presenter: Dr. Udita Katugampola, on March 4, 2016, 11:20 am @336
Title: What is a fractional derivative?
Abstract: In this tutorial seminar, we will introduce the concept of fractional derivatives along with some historical backgrounds. We will talk about several approaches to form several different fractional derivatives. Among such derivatives, we will spend some time for the Riemann-Liouville derivative, Caputo derivative, Hadamard derivative, and finally Katugampola derivative. We will then talk about what we mean by a fractional differential equation and some approaches to such differential equations. One of the main goals of the talk is to motivate students for research work in this beautiful realm of research. Slides
Presenter: Dr. Linde Werner, on March 10, 2016, 1:00 pm @336
Title: Fractional Integration with Varying Smoothness
Presenter: Ryan Evans, on March 24, 2016, 1:00pm @336
Title: Biochemical Reactions: An Application of Fractional Calculus
Abstract: Many chemical reactions in nature involve a stream of chemical reactants flowing through a fluid-filled volume, over a surface to which other reactants are confined. Examples include blood clotting and drug absorption. These reactions, referred to as surface-volume reactions, are a natural application of fractional calculus. We will discuss a mathematical model for surface-volume reactions, and how this model led to a new result in fractional integral equations.
Presenter: Dr. Linde Werner, on November 28, 2016, 2:30pm @336
Title: Gaussian Processes generated by Linear Operators – The Riemann-Liouville Process
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