A note on one-dimensional time fractional ODEs
© 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. . 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.
Feng, Y; Li, L; Liu, JG; Xu, X
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