FRACTIONAL INTEGRO-DIFFERENTIATION ON THE SEMI-AXIS, INVARIANT WITH RESPECT TO A DILATATION
The paper introduces the concept of a difference of fractional order with a multiplicative step and its features. We consider “convolution type” operators that are invariant with respect to a dilatation and to their approximation using units in weighted Lebesgue spaces. It is shown that the domains of two different fractional differentiations considered here of the Marchaud-Hadamard type and the GrunwaldLetnikov-Hadamard type coincide in piecewise-power weighted spaces of summable functions.