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Wave process in viscoelastic media using fractional derivatives with nonsingular kernels.

Authors :
Antonio Taneco‐Hernández, Marco
Gómez‐Aguilar, José Francisco
Cuahutenango‐Barro, Bricio
Source :
Mathematical Methods in the Applied Sciences. Mar2023, Vol. 46 Issue 4, p4413-4436. 24p.
Publication Year :
2023

Abstract

We consider the equations of motion of a bar, with given density, infinite in both directions, subjected to longitudinal vibrations under the action of an external load, and a stress–strain relation represented by a fractional‐order operator. Using three types of fractional operators, the initial‐boundary value problems associated with the described phenomenon are posed and solved. Through the bivariate Mittag–Leffer function, which has been recently introduced, we find the fundamental solution of these problems and calculate their moments. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
01704214
Volume :
46
Issue :
4
Database :
Academic Search Index
Journal :
Mathematical Methods in the Applied Sciences
Publication Type :
Academic Journal
Accession number :
161743354
Full Text :
https://doi.org/10.1002/mma.8767