Regularized fractional derivatives in Colombeau algebra

Document Type : Research Paper


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

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


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.

  • Receive Date: 19 March 2014
  • Revise Date: 10 May 2015
  • Accept Date: 25 October 2015
  • First Publish Date: 18 February 2016