%0 Journal Article
%T Regularized fractional derivatives in Colombeau algebra
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Alimohammady, Mohsen
%A Fattahi Amirdehi, Fariba
%D 2016
%\ 01/01/2016
%V 7
%N 1
%P 279-287
%! Regularized fractional derivatives in Colombeau algebra
%R 10.22075/ijnaa.2015.147
%X 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 ofÂ 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.
%U https://ijnaa.semnan.ac.ir/article_147_ab2bc88c6c15434692b835d36280d41a.pdf