TY  - JOUR
A1  - Mainardi, Francesco
A1  - Consiglio, Armando
T1  - The Wright Functions of the Second Kind in Mathematical Physics
T2  - Mathematics
N2  - In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.
KW  - fractional calculus
KW  - Wright functions
KW  - Green’s functions
KW  - diffusion-wave equation
KW  - Laplace transform
Y1  - 2020
UR  - https://opus.bibliothek.uni-wuerzburg.de/frontdoor/index/index/docId/20778
UR  - https://nbn-resolving.org/urn:nbn:de:bvb:20-opus-207782
SN  - 2227-7390
VL  - 8
IS  - 6
ER  -