We study the asymptotic behavior of Timoshenko systems with a fractional operator in the memory term depending on a parameter.. 0, 1 and acting only on one equation of the system. Considering exponentially decreasing kernels, we find exact decay rates. To be precise, we show that for.. 0, 1), the system decay polynomially with rates that depend on the value of the difference of the wave propagation speeds. We also prove that these decay rates are optimal. Moreover, when. = 1 and the equations have the same propagation speeds we obtain the exponential decay of the solutions.
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