We show that the anomalous diffusion equations with a fractional spatial derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the Lévy stable distributions which stem from the evolution properties of stretched or compressed exponential function. The formal solutions of these fractional differential equations are found by using the evolution operator method where the evolution is conceived as integral transform whose kernel is the Green function. Exact and explicit examples of the solutions are reported and studied for various fractional order of derivatives and for different initial conditions. © 2017 Diogenes Co., Sofia 2017.

The stretched exponential behavior and its underlying dynamics. the phenomenological approach

Dattoli, G.
2017

Abstract

We show that the anomalous diffusion equations with a fractional spatial derivative in the Caputo or Riesz sense are strictly related to the special convolution properties of the Lévy stable distributions which stem from the evolution properties of stretched or compressed exponential function. The formal solutions of these fractional differential equations are found by using the evolution operator method where the evolution is conceived as integral transform whose kernel is the Green function. Exact and explicit examples of the solutions are reported and studied for various fractional order of derivatives and for different initial conditions. © 2017 Diogenes Co., Sofia 2017.
Green functions;stretched or compressed exponential function;fractional ordinary and partial differential equations;fractional calculus
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12079/1775
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