| Summary: | This paper is concerned with the nonexistence of global solutions to fractional in time nonlinear Schrödinger equations of the form <inline-formula> <math display="inline"> <semantics> <mrow> <msup> <mi>i</mi> <mi>α</mi> </msup> <msubsup> <mo>∂</mo> <mi>t</mi> <mi>α</mi> </msubsup> <mi>ω</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>Δ</mo> <mi>ω</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mi>i</mi> <mi>α</mi> </msup> <msub> <mi>a</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mi>ω</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>ξ</mi> <msup> <mrow> <mo>|</mo> <mi>ω</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mi>p</mi> </msup> <mo>,</mo> <mspace width="1.em"></mspace> <mrow> <mo>(</mo> <mi>t</mi> <mo>,</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>∈</mo> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mo>∞</mo> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mi mathvariant="double-struck">R</mi> <mi>N</mi> </msup> </mrow> </semantics> </math> </inline-formula>, where <inline-formula> <math display="inline"> <semantics> <mrow> <mi>N</mi> <mo>≥</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mrow> <mi>ξ</mi> <mo>∈</mo> <mi mathvariant="double-struck">C</mi> <mo>\</mo> <mo>{</mo> <mn>0</mn> <mo>}</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mi>p</mi> <mo>></mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>, under suitable initial data. To establish our nonexistence theorem, we adopt the Pohozaev nonlinear capacity method, and consider the combined effects of absorption and dispersion terms. Further, we discuss in details some special cases of coefficient functions <inline-formula> <math display="inline"> <semantics> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>∈</mo> <msubsup> <mi>L</mi> <mrow> <mi>l</mi> <mi>o</mi> <mi>c</mi> </mrow> <mn>1</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mo>∞</mo> <mo>)</mo> </mrow> <mo>,</mo> <mi mathvariant="double-struck">R</mi> <mo>)</mo> </mrow> </mrow> </semantics> </math> </inline-formula>, and provide two illustrative examples.
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