Introduction to Fractional Calculus

"Introduction to Fractional Calculus" is a forthcoming free-of-charge course offered by prof. A. I. Fedorchenko. The objective of the couse is to provide its participants with the background necessary for the understanding of the fractional calculus. The lectures will be given in English in the Institute of Thermomechanics ASCR, v. v. i.. The dates and times will be announced at a later date based on the response received.

The course starts on November 9, 2009 and will be held every Monday until December 28, 2009*.
The lectures will be given in the Lecture room B at 10:00-11:30*.

*Preliminary, subject to change.

Abstract: This course starts from scratch and provides students with the background necessary for the understanding of the fractional calculus. It is surprisingly, but most scientists and engineers remain unaware of Fractional Calculus; it is not being taught in schools and colleges; and others remain skeptical of this field. There are several reasons for that: several of the definitions proposed for fractional derivatives were inconsistent, meaning they worked in some cases but not in others. The mathematics involved appeared very different from that of integer order. There were almost no practical applications of this field, and it was considered by many as an abstract area containing only mathematical manipulations of little or no use. But recently, the paradigm began to shift from pure mathematical formulation to applications in various fields. During the last decade Fractional Calculus has been applied to almost every field of science, engineering, and mathematics. Some of the areas where Fractional Calculus has made a profound impact include viscoelasticity and rheology, electrical engineering, electrochemistry, biology, biophysics and bioengineering, signal and image processing, mechanics, mechatronics, physics, and control theory.

Alexander I. Fedorchenko received his Ph.D. degree in Thermophysics and Molecular Physics in 1991 and the Doctor of Physical and Mathematical Sciences degree in 2000, both from the Institute of Thermophysics of Siberian Branch of the Russian Academy of Sciences (Novosibirsk). He became an associate professor in 1991. In 2001 he was appointed a leading scientist at the Department of Physical Hydrodynamics, Institute of Thermophysics. From 2001 till 2009 he was working in the Institute of Applied Mechanics, National Taiwan University, ROC. In 2009, he joined the Institute of Thermomechanics, Academy of Sciences of the Czech Republic. He is an editor of three books: “High-Temperature Dust-Laden Jets in Plasma Technology,” (co-ed. O. P. Solonenko), VSP, Utrecht, The Netherlands, Tokyo, Japan, 1990, 571 p., “Plasma Jets in the Development of New Materials Technology,” (co-ed. O. P. Solonenko), VSP, Utrecht, The Netherlands, Tokyo, Japan, 1990, 716 p., “High Velocity Acceleration of Macrobody,” (co-ed. A. S. Anshakov) NOVA Science Publisher Inc., New York, 1994, 200 p. He was a member of the organizing committee of international and Russian workshops and conferences. He is also reviewer of many international academic journals.

In 2008 he delivered a course “Introduction to Fractional Calculus” in Huafan University, Taiwan, R. O. C and Yuan Ze University, Taiwan, R. O. C. His research interests cover drop impact on liquid and solid surfaces, heat and mass transfer in a granular medium, fractional calculus, thermo- and concentration-capillary convection in thin film, equilibrium and non-equilibrium crystallization, analytical and asymptotical methods for solving of the conjugate heat transfer problems, modal analysis of mechanical systems with piecewise constant properties, wrinkling of free-standing nanofilms.

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