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Wave process in viscoelastic media using fractional derivatives with non singular kernels
  • J. F. Gómez-Aguilar,
  • Bricio Cuahutenago-Barro
Autonomous University of Guerrero

Corresponding Author:mataneco@uagro.mx

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J. F. Gómez-Aguilar
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Bricio Cuahutenago-Barro
Autonomous University of Guerrero
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In this paper, we consider the equations of motion of a bar, of a given density, infinite in both direction, undergoing longitudinal vibrations under the action of an external load, and a stress-strain relationship using a fractional order differentiation operator with respect to the time variable. We use three types of fractional operators, two non-singular, one with exponential kernel and Mittag-Leffler type kernel. And a singular one with power-law type kernel. We analyze some initial and boundary value problems resulting from the modeling of the aforementioned wave processes in viscoelastic media, using some recent proposals for fractional order derivatives. The fundamental solution of these problems is established, and its moments are calculated.
19 Jan 2022Submitted to Mathematical Methods in the Applied Sciences
20 Jan 2022Submission Checks Completed
20 Jan 2022Assigned to Editor
22 Jan 2022Reviewer(s) Assigned
13 Jun 2022Review(s) Completed, Editorial Evaluation Pending
15 Jun 2022Editorial Decision: Revise Major
17 Sep 20221st Revision Received
19 Sep 2022Submission Checks Completed
19 Sep 2022Assigned to Editor
20 Sep 2022Reviewer(s) Assigned
20 Sep 2022Review(s) Completed, Editorial Evaluation Pending
21 Sep 2022Editorial Decision: Accept