  This paper is devoted to the solution and stability of a one-dimensional
model depicting Rao--Nakra sandwich beams, incorporating damping terms
characterized by fractional derivative types within the domain, specifically a
generalized Caputo derivative with exponential weight. To address existence,
uniqueness, stability, and numerical results, fractional derivatives are
substituted by diffusion equations relative to a new independent variable,
$\xi$, resulting in an augmented model with a dissipative semigroup operator.
Polynomial decay of energy is achieved, with a decay rate depending on the
fractional derivative parameters. Both the polynomial decay and its dependency
on the parameters of the generalized Caputo derivative are numerically
validated. To this end, an energy-conserving finite difference numerical scheme
is employed.
