Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#335603] of Jian-Guo Liu

Papers Published

  1. Feng, Y; Li, L; Liu, JG; Xu, X, A note on one-dimensional time fractional ODEs, Applied Mathematics Letters, vol. 83 (September, 2018), pp. 87-94, Elsevier BV [doi]
    (last updated on 2019/05/21)

    © 2018 Elsevier Ltd In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work Feng et al. [15]. Here we use the definition of Caputo derivative proposed in Li and Liu (2017) [5,7] based on a convolution group. In particular, we establish generalized comparison principles consistent with the new definition of Caputo derivatives. In addition, we establish the full asymptotic behaviors of the solutions for D cγ u=Au p . Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320