Wave process in viscoelastic media using fractional derivatives with non singular kernels
- MARCO ANTONIO TANECO-HERNANDEZ
, - J F Gómez-Aguilar,
- B Cuahutenango-Barro
MARCO ANTONIO TANECO-HERNANDEZ
![](https://d197for5662m48.cloudfront.net/assets/icons/omniauth/orcid-ca37582cd91a671ed5cec57770e0e96c01b4b79b8b5b75d8598fc1ddac18c974.svg)
Facultad de Matemáticas, Universidad Autónoma de Guerrero. Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo
Corresponding Author:[email protected]
Author ProfileJ F Gómez-Aguilar
CONACyT-Tecnológico Nacional de México/CENIDET. Interior Internado Palmira S/N
B Cuahutenango-Barro
Facultad de Matemáticas, Universidad Autónoma de Guerrero. Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo
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.