Space–time fractional Zener wave equation-Reference-Cited by-同舟云学术

Space–time fractional Zener wave equation

Published:2015-02 Issue:2174 Volume:471 Page:20140614
ISSN:1364-5021
Container-title:Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
language:en
Short-container-title:Proc. R. Soc. A.

Author:

Atanackovic T.M.¹,Janev M.²,Oparnica Lj.³,Pilipovic S.⁴,Zorica D.²^ORCID

Affiliation:

1. Department of Mechanics, Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovica 6, 21000 Novi Sad, Serbia

2. Mathematical Institute, Serbian Academy of Arts and Sciences, Kneza Mihaila 36, 11000 Belgrade, Serbia

3. Faculty of Education in Sombor, University of Novi Sad, Podgorička 4, 25000 Sombor, Serbia

4. Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Novi Sad, Trg D. Obradovica 4, 21000 Novi Sad, Serbia

Abstract

The space–time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analysed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented.

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

Link

https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.2014.0614

Reference45 articles.

1. Distributed order calculus and equations of ultraslow diffusion

2. Some aspects of fractional diffusion equations of single and distributed order;Mainardi F;Appl. Math. Comput.,2007

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