What is a fractional derivative?

Manuel Duarte Ortigueira, J. A. Tenreiro Machado. What is a fractional derivative?. J. Comput. Physics, 293:4-13, 2015. [doi]

@article{OrtigueiraM15,
  title = {What is a fractional derivative?},
  author = {Manuel Duarte Ortigueira and J. A. Tenreiro Machado},
  year = {2015},
  doi = {10.1016/j.jcp.2014.07.019},
  url = {http://dx.doi.org/10.1016/j.jcp.2014.07.019},
  researchr = {https://researchr.org/publication/OrtigueiraM15},
  cites = {0},
  citedby = {0},
  journal = {J. Comput. Physics},
  volume = {293},
  pages = {4-13},
}