The Wright functions of the second kind in Mathematical Physics

Abstract

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. Keywords: Fractional Calculus, Wright Functions, Green's Functions, Diffusion-Wave Equation,

arXiv comment31 pages, 10 figures

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• Distributed Order Calculus and Equations of Ultraslow Diffusion
• Leapover lengths and first passage time statistics for Lévy flights
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• A Tutorial on the Basic Special Functions of Fractional Calculus
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• Differentiation of the Wright functions with respect to parameters and other results
• Single-file dynamics with general charge measures
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