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.
Alimohammady,M and Fattahi Amirdehi,F . (2016). Regularized fractional derivatives in Colombeau algebra. International Journal of Nonlinear Analysis and Applications, 7(1), 279-287. doi: 10.22075/ijnaa.2015.147
MLA
Alimohammady,M , and Fattahi Amirdehi,F . "Regularized fractional derivatives in Colombeau algebra", International Journal of Nonlinear Analysis and Applications, 7, 1, 2016, 279-287. doi: 10.22075/ijnaa.2015.147
HARVARD
Alimohammady M, Fattahi Amirdehi F. (2016). 'Regularized fractional derivatives in Colombeau algebra', International Journal of Nonlinear Analysis and Applications, 7(1), pp. 279-287. doi: 10.22075/ijnaa.2015.147
CHICAGO
M Alimohammady and F Fattahi Amirdehi, "Regularized fractional derivatives in Colombeau algebra," International Journal of Nonlinear Analysis and Applications, 7 1 (2016): 279-287, doi: 10.22075/ijnaa.2015.147
VANCOUVER
Alimohammady M, Fattahi Amirdehi F. Regularized fractional derivatives in Colombeau algebra. IJNAA. 2016;7(1):279-287. doi: 10.22075/ijnaa.2015.147
International Journal of Nonlinear Analysis and Applications