We study the nonexistence of global weak solutions to the following semi-linear Moore – Gibson-
Thompson equation with the nonlinearity of derivative type, namely,
{uttt+utt−Δu−(−Δ)α2ut=|ut|p,x∈\Rn,t>0,u(0,x)=u0(x),ut(0,x)=u1(x),utt(0,x)=u2(x)x∈\Rn,
where α∈(0,2],p>1, and (−Δ)α2 is the fractional Laplacian operator of order α2. Then, this result is extended to the case of a weakly coupled
system. We intend to apply the method of a modified test function to establish nonexistence results and to overcome some difficulties as well caused by the well-known fractional Laplacian (−Δ)α2.The results obtained in this paper extend several contributions in this field.