## A note on one-dimensional time fractional ODEs

Publication
, Journal Article

Feng, Y; Li, L; Liu, JG; Xu, X

Published in: Applied Mathematics Letters

September 1, 2018

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 Dcγu=Aup. Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions.

### Duke Scholars

## Published In

Applied Mathematics Letters

## DOI

## EISSN

1873-5452

## ISSN

0893-9659

## Publication Date

September 1, 2018

## Volume

83

## Start / End Page

87 / 94

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics

### Citation

APA

Chicago

ICMJE

MLA

NLM

Feng, Y., Li, L., Liu, J. G., & Xu, X. (2018). A note on one-dimensional time fractional ODEs.

*Applied Mathematics Letters*,*83*, 87–94. https://doi.org/10.1016/j.aml.2018.03.015Feng, Y., L. Li, J. G. Liu, and X. Xu. “A note on one-dimensional time fractional ODEs.”

*Applied Mathematics Letters*83 (September 1, 2018): 87–94. https://doi.org/10.1016/j.aml.2018.03.015.Feng Y, Li L, Liu JG, Xu X. A note on one-dimensional time fractional ODEs. Applied Mathematics Letters. 2018 Sep 1;83:87–94.

Feng, Y., et al. “A note on one-dimensional time fractional ODEs.”

*Applied Mathematics Letters*, vol. 83, Sept. 2018, pp. 87–94.*Scopus*, doi:10.1016/j.aml.2018.03.015.Feng Y, Li L, Liu JG, Xu X. A note on one-dimensional time fractional ODEs. Applied Mathematics Letters. 2018 Sep 1;83:87–94.

## Published In

Applied Mathematics Letters

## DOI

## EISSN

1873-5452

## ISSN

0893-9659

## Publication Date

September 1, 2018

## Volume

83

## Start / End Page

87 / 94

## Related Subject Headings

- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics