The Nonexistence of Global Solutions for a Time Fractional Schrödinger Equation with Nonlinear Memory - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.7, July 2018

Journal of Applied Mathematics and Physics

Volume 6, Issue 7 (July 2018)

ISSN Print: 2327-4352 ISSN Online: 2327-4379

Google-based Impact Factor: 0.70 Citations

The Nonexistence of Global Solutions for a Time Fractional Schrödinger Equation with Nonlinear Memory ()

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DOI: 10.4236/jamp.2018.67118 868 Downloads 1,505 Views

Author(s)

Yaning Li^1*, Quanguo Zhang²

Affiliation(s)

¹College of Mathematics & Statistics, Nanjing University of Information Science & Technology, Nanjing, China.
²Department of Mathematics, Luoyang Normal University, Luoyang, Henan, China.

ABSTRACT

In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory

where 0<λ<β<1, ι^λ denotes the principal value of ι^λ, 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.

KEYWORDS

Fractional Schrödinger Equation, Nonexistence, Cauchy Problems, Nonlinear Memory

Share and Cite:

Li, Y. and Zhang, Q. (2018) The Nonexistence of Global Solutions for a Time Fractional Schrödinger Equation with Nonlinear Memory. Journal of Applied Mathematics and Physics, 6, 1418-1424. doi: 10.4236/jamp.2018.67118.

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