Compositional Structure of Classical Integral Transforms

Oleg Marichev

The fractional order integro-differentiation operator FractionalD is a particular case of some more general integral transforms. Using MellinTransform, one can construct two main classes of integral transforms: convolution type and those with respect to indices. We give definitions, inversions, compositional structure, and representations through more general transforms. Some can be directly applied to rational and other functions representable through MeijerG functions.