Preprint Article Version 1 This version not peer reviewed

On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equatio

Version 1 : Received: 11 November 2017 / Approved: 12 November 2017 / Online: 12 November 2017 (08:30:34 CET)

A peer-reviewed article of this Preprint also exists.

Luchko, Y. On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation. Mathematics 2017, 5, 76. Luchko, Y. On Some New Properties of the Fundamental Solution to the Multi-Dimensional Space- and Time-Fractional Diffusion-Wave Equation. Mathematics 2017, 5, 76.

Journal reference: Mathematics 2017, 5, 76
DOI: 10.3390/math5040076

Abstract

In this paper, some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation are deduced. We start with the Mellin-Barnes representation of the fundamental solution that was derived in the previous publications of the author. The Mellin-Barnes integral is used to get two new representations of the fundamental solution in form of the Mellin convolution of the special functions of the Wright type. Moreover, some new closed form formulas for particular cases of the fundamental solution are derived. In particular, we solve an open problem of representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions.

Subject Areas

multi-dimensional diffusion-wave equation; neutral-fractional diffusion-wave equation; fundamental solution; Mellin-Barnes integral; integral representation; Wright function; generalized Wright function

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