# Time-fractional diffusion equation and its applications in physics

Consiglio, Armando (2017) Time-fractional diffusion equation and its applications in physics. [Laurea], Università di Bologna, Corso di Studio in Fisica [L-DM270]
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## Abstract

In physics, process involving the phenomena of diffusion and wave propagation have great relevance; these physical process are governed, from a mathematical point of view, by differential equations of order 1 and 2 in time. By introducing a fractional derivatives of order $\alpha$ in time, with $0 < \alpha < 1$ or $1 <= \alpha <= 2$, we lead to process in mathematical physics which we may refer to as fractional phenomena; this is not merely a phenomenological procedure providing an additional fit parameter. The aim of this thesis is to provide a description of such phenomena adopting a mathematical approach to the fractional calculus. The use of Fourier-Laplace transform in the analysis of the problem leads to certain special functions, scilicet transcendental functions of the Wright type, nowadays known as M-Wright functions. We will distinguish slow-diffusion processes ($0 < \alpha < 1$) from intermediate processes ($1 <=\alpha <= 2$), and we point out the attention to the applications of fractional calculus in certain problems of physical interest, such as the Neuronal Cable Theory.

Abstract
Tipologia del documento
Tesi di laurea (Laurea)
Autore della tesi
Consiglio, Armando
Relatore della tesi
Correlatore della tesi
Scuola
Corso di studio
Ordinamento Cds
DM270
Parole chiave
Diffusion,Laplace,Fractional calculus,Cable equation,Biophysics
Data di discussione della Tesi
14 Luglio 2017
URI