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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
Facultad de Matemáticas, Universidad Autónoma de Guerrero. Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo

Corresponding Author:[email protected]

Author Profile
J 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.