Calculus on Fractal Curves in R^n and Physical Applications

by Dr Seema Satin (University of Pune)

Wednesday 5 Jan 2011, 14:30 → 15:30 Asia/Kolkata

A-304 (Colaba Campus)

I will present an overview of a new Calculus on fractal curves, which will begin with defining a mass function on fractal curves. This mass function will then be used to define new integrals and derivatives, namely the $F^\alpha$-integral and differential operators. Thus after presenting a newly developed Calculus for fractal curves, I will talk about a conjugacy between this and Riemann Calculus which gives a method to evaluate $F^\alpha$ integral and derivatives for many simple cases. In the second part of my talk, I will discuss and demonstate some Physical applications of $F^\alpha$ Calculus. This will include Fokker-Planck Equation, Random walk problems and the Langevin approach on fractal curves. Some interesting results obtained by exact or heuristic methods, regarding the above Physical Applications will be presented.