Wave process in viscoelastic media using fractional derivatives with nonsingular kernels

摘要

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.