A note on one-dimensional time fractional ODEs
Classical Analysis and ODEs
2018-04-03 v2
Abstract
In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017} 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 . Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions.
Cite
@article{arxiv.1712.08956,
title = {A note on one-dimensional time fractional ODEs},
author = {Yuanyuan Feng and Lei Li and Jian-Guo Liu and Xiaoqian Xu},
journal= {arXiv preprint arXiv:1712.08956},
year = {2018}
}