Special Functions Of Fractional Calculus. Applications to Diffusion and Random Search Processes

Investigation of stochastic processes in complex media has been at-
tracted much attention for years.
Theoretical modeling of diffusion in
heterogeneous and disordered media is a considerable part of these stud-
ies. Heterogeneous and disordered materials include various materials with
defects, multi-scale amorphous composites, fractal and sparse structures,
weighted graphs and networks, and so on. Diffusion in such complicated
media with geometric constraint and random forces is often anomalous.
Further developing of the theory for understanding and description of these
random processes in a variety of realizations in physics, biology, social life
and finance is a part of modern studies, what we called “complex systems”.
These complex phenomena entailing complex descriptions by fractional ki-
netics and fractional calculus.