On the Fractional Derivative Duality in Some Transforms

Duality is one of the most interesting properties of the Laplace and Fourier transforms associated with the integer-order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier transforms. The scale and nabla derivatives are used. Some consequences are described.

Automated summary

This article introduces the duality of Laplace and Fourier transforms associated with integer-order derivatives and generalizes it to fractional derivatives. The results are further extended to other transforms such as Mellin, Z, and discrete-time Fourier transforms. The use of scale and nabla derivatives and some consequences are also described.