Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

Abstract

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C^∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.