A note on one-dimensional time fractional ODEs

Published

Journal Article

© 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.

Full Text

Duke Authors

Cited Authors

  • Feng, Y; Li, L; Liu, JG; Xu, X

Published Date

  • September 1, 2018

Published In

Volume / Issue

  • 83 /

Start / End Page

  • 87 - 94

Electronic International Standard Serial Number (EISSN)

  • 1873-5452

International Standard Serial Number (ISSN)

  • 0893-9659

Digital Object Identifier (DOI)

  • 10.1016/j.aml.2018.03.015

Citation Source

  • Scopus