Positive time fractional derivative
<|reference_start|>Positive time fractional derivative: In mathematical modeling of the non-squared frequency-dependent diffusions, also known as the anomalous diffusions, it is desirable to have a positive real Fourier transform for the time derivative of arbitrary fractional or odd integer order. The Fourier transform of the fractional time derivative in the Riemann-Liouville and Caputo senses, however, involves a complex power function of the fractional order. In this study, a positive time derivative of fractional or odd integer order is introduced to respect the positivity in modeling the anomalous diffusions.<|reference_end|>
@article{chen2002positive,
    title={Positive time fractional derivative},
    author={W Chen},
    journal={arXiv preprint arXiv:cs/0210005},
    year={2002},
    number={Simula Research Laboratory Report, Sept. 2002},
    archivePrefix={arXiv},
    eprint={cs/0210005},
    primaryClass={cs.CE}
}