Nonexistence of global solutions for fractional temporal schrödinger equations and systems

We, first, consider the nonlinear Schrödinger equation (Formula Presented)where 0 < α < 1, iα is the principal value of (Formula Presented) is the Caputo fractional derivative of order (Formula Presented) is a complex-valued function, and a: ℝN→ ℝN is a given vector function. We provide suffcient conditions for the nonexistence of global weak solution under suitable initial data. Next, we extend our study to the system of nonlinear coupled equations (Formula Presented) where (Formula Presented), and a; b: ℝN → ℝ N are two given vector functions. Our approach is based on the test function method. ©2017 Texas State University.