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Fractional Calculus: some topics from modeling, numerics and analytics.
Fractional differential equations are more and more used to model
the phenomena that usual differential equations can not model, since the
traditional derivatives are local properties. At the same time the behavior
of the solution is often determined not only by the nearby points, but
by points in the whole domain and fractional derivatives present a way
to capture it. In this talk we consider three problems related to
fractional differential equations:
1). Discussion on derivation of a fractional conservation of mass
equation from the first principles.
2). Fast numerical algorithm for the linear fractional advection-diffusion
equations with nonlinear reaction term.
3). Approximate analytical solution to the time-fractional porous
This is a joint work with Jeffrey Olsen, Anthony LaFleur, Emine Celik and