L. Plociniczak (Wroclaw University of Technology)
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During the last few decades a rapid growth of methods and models based on
differential equations of arbitrary order has been observed. This research is,
as almost always, motivated in a twofold way - both by the pure mathematical
curiosity and by physical phenomena, which adequate description is beyond the
classical mathematical modelling. Some of these investigations have given a
need for generalizations of the notion of integral and derivative. During this
talk I plan to investigate a problem associated with the analysis of
differential equations with the fractional derivative. This will be based on my
previously published results which develop appropriate mathematical tools and
methods. Their main purpose is to transform an integral equation with the
fractional derivative into a classical ordinary differential equation. This
equation, although more simple, usually cannot be solved analytically. My
approach is based on an application of a number of approximation methods such
as asymptotic expansions and perturbation theory.