Generalized wave equation in nonlocal elasticity

We study the motion of a one-dimensional continuum whose deformation is described by a strain measure of nonlocal type. In particular, we use the Caputo fractional derivatives and a linear relation between stress and strain measure to obtain an integro-differential equation of motion. This equation is solved in the space of tempered distributions by using the Fourier and Laplace transforms. The properties of the solution are examined and compared with the classical case.