Open AccessFractional derivatives of Colombeau generalized stochastic processes defined on R+
Author(s) -
Danijela Rajter-Ćirić
Publication year - 2011
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm110824020r
Subject(s) - mathematics , generalized function , fractional calculus , pure mathematics , cauchy distribution , mathematical analysis
We consider Caputo and Riemann-Liouville fractional derivatives of a Colombeau generalized stochastic process $G$ defined on ${mathbb R}^+$. We give proper definitions and prove that both are Colombeau generalized stochastic processes themselves. We also give a solution to a certain Cauchy problem illustrating the application of the theory