Cauchy problem with Riesz operator of fractional differentiation - Litovchenko, V. A. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
In the class of generalized functions of finite order, we establish the correct solvability of the Cauchy problem for a pseudodifferential equation whose symbols are homogeneous functions of order γ > 0. We prove a theorem on the localization property of a solution of this problem.