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arXiv · 1712.08956

A note on one-dimensional time fractional ODEs

Yuanyuan Feng·Lei Li·Jian-Guo Liu·Xiaoqian Xu
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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 $D_c^γu=Au^p$. Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions.

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Yuanyuan Feng, Lei Li, Jian-Guo Liu, Xiaoqian Xu. 2018-04-01. A note on one-dimensional time fractional ODEs. https://arxiv.org/abs/1712.08956

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