Semnan University
International Journal of Nonlinear Analysis and Applications
2008-6822
7
1
2016
01
01
Regularized fractional derivatives in Colombeau algebra
279
287
147
10.22075/ijnaa.2015.147
EN
Mohsen
Alimohammady
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Fariba
Fattahi Amirdehi
Department of mathematics, University of Mazandaran, babolsar, Iran
Journal Article
2014
03
19
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.
https://ijnaa.semnan.ac.ir/article_147_ab2bc88c6c15434692b835d36280d41a.pdf