Study of some evolution equations involving Riesz fractional derivative with singular initial data

Abstract

The objective of this work is to study some evolution problems involving the Riesz fractional derivative with singular initial data which can be distributions. It is a question of proving the existence and uniqueness of the solutions of these problems in the extended Colombeau algebra GeR . It is established that the existence and uniqueness generalized solutions hold for both evolution problems associated to the Schr¨odinger equation and the heat equation involving the corresponding Riesz fractiononal operators derivatives.