Regularized fractional derivatives in Colombeau algebra

Document Type: Research Paper

Authors

1 Department of Mathematics, University of Mazandaran, Babolsar, Iran

2 Department of mathematics, University of Mazandaran, babolsar, Iran

Abstract

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to a nonlinear heat equation illustrating the application of the theory.