TITLE:
The Nonexistence of Global Solutions for a Time Fractional Schrödinger Equation with Nonlinear Memory
AUTHORS:
Yaning Li, Quanguo Zhang
KEYWORDS:
Fractional Schrödinger Equation, Nonexistence, Cauchy Problems, Nonlinear Memory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.7,
July
10,
2018
ABSTRACT: In this paper, we study the nonexistence of solutions of the
following time fractional nonlinear Schr?dinger equations with nonlinear memory
where 0, ιλ denotes the principal
value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value
function, denotes left
Riemann-Liouville fractional integrals of order 1-λ and is the Caputo
fractional derivative of order . We obtain that the problem admits no global weak solution
when and under different
conditions for initial data.