In this paper, we study the following time fractional Schrödinger equation
where 81a282cc7d7f8eee6010953e079aa33" title="Click to view the MathML source">0<α<1, bf51547ea834cb3bc4e3a04873c3" title="Click to view the MathML source">iα denotes the principal value of bf51547ea834cb3bc4e3a04873c3" title="Click to view the MathML source">iα, T>0, bf7cfa77999c60c497aa908" title="Click to view the MathML source">λ∈C∖{0}, e7a444d1e4e8d4d8a" title="Click to view the MathML source">p>1, 81f9cbfdbc" title="Click to view the MathML source">u(t,x) is a complex-valued function, and denotes Caputo fractional derivative of order α. We prove that the problem admits no global weak solution with suitable initial data when e773f122f478ed5a21ae8e733bba976" title="Click to view the MathML source">1<p<1+2∕N by using the test function method, and also give some conditions which imply the problem has no global weak solution for every e7a444d1e4e8d4d8a" title="Click to view the MathML source">p>1.