In this paper,
we study the follo
wing time fractional Schr&
ouml;dinger equation
where
k to view the MathML source">0<α<1,
k to view the MathML source">iα denotes the principal value of
k to view the MathML source">iα,
k to view the MathML source">T>0,
k to view the MathML source">λ∈C∖{0},
k to view the MathML source">p>1,
k to view the MathML source">u(t,x) is a complex-valued function, and
w the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S089396591630252X&_mathId=si9.gif&_user=111111111&_pii=S089396591630252X&_rdoc=1&_issn=08939659&md5=4be8077617b25440d2744a224cc1c946">
width="35" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S089396591630252X-si9.gif"> denotes Caputo fractional derivative of order
k to view the MathML source">α. We prove that the problem admits no global
wea
k solution
with suitable initial data
when
k 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
wea
k solution for every
k to view the MathML source">p>1.