In this paper, we study the semilinear equation with a time fractional structural damping Dβ0|tu(t,x)−2∆Dα0|tu(t,x)+∆2u(t,x) = |u(t,x)|p t > 0, x ∈ Ω,
where p > 1, 1 < α < 1 < β < 2 and Dα is the Caputo fractional derivative. We obtain the blow- up result under some positive data 2 0|t
when 1 < p < 1+ 2α . Whereas, if p 1+ 2α and ∥u0∥L2qc (Ω), qc = N(p−1)/4 is sufficiently small, we prove the existence of global solution.
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