The quantum fractional derivative is defined using formulations analogue to the common Grünwald-Letnikov derivatives. While these use a linear variable scale, the quantum derivative uses an exponential scale and is defined inR+orR-. Two integral formulations similar to the usual Liouville derivatives are deduced with the help of the Mellin transform.
|Journal||Communications In Nonlinear Science And Numerical Simulation|
|Publication status||Published - 1 Jan 2010|
Ortigueira, M. D., & DEE Group Author (2010). The fractional quantum derivative and its integral representations. Communications In Nonlinear Science And Numerical Simulation, 15(4), 956-962. https://doi.org/10.1016/j.cnsns.2009.05.026