Next Article in Journal
Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme
Next Article in Special Issue
An Iterative Method for Solving a Class of Fractional Functional Differential Equations with “Maxima”
Previous Article in Journal
Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras
Previous Article in Special Issue
Fractional Derivatives, Memory Kernels and Solution of a Free Electron Laser Volterra Type Equation
Article Menu
Issue 4 (December) cover image

Export Article

Open AccessArticle
Mathematics 2017, 5(4), 76; https://doi.org/10.3390/math5040076

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

Beuth University of Applied Sciences Berlin, 13353 Berlin, Germany
Current address: Beuth Hochschule für Technik Berlin, Fachbereich II Mathematik-Physik-Chemie, Luxemburger Str. 10, 13353 Berlin, Germany.
Received: 11 November 2017 / Revised: 1 December 2017 / Accepted: 4 December 2017 / Published: 8 December 2017
(This article belongs to the Special Issue Fractional Calculus: Theory and Applications)
View Full-Text   |   Download PDF [275 KB, uploaded 8 December 2017]

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 obtain two new representations of the fundamental solution in the 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 the open problem of the representation of the fundamental solution to the two-dimensional neutral-fractional diffusion-wave equation in terms of the known special functions. View Full-Text
Keywords: multi-dimensional diffusion-wave equation; neutral-fractional diffusion-wave equation; fundamental solution; Mellin-Barnes integral; integral representation; Wright function; generalized Wright function multi-dimensional diffusion-wave equation; neutral-fractional diffusion-wave equation; fundamental solution; Mellin-Barnes integral; integral representation; Wright function; generalized Wright function
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
SciFeed

Share & Cite This Article

MDPI and ACS Style

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top