Extension of Colombeau algebra to derivatives of arbitrary order D\(^\alpha ,\alpha \in \mathbf R_+ \cup \{0\}\). Application to ODEs and PDEs with entire and fractional derivatives
type: Item
instance of: scholarly article
title: Extension of Colombeau algebra to derivatives of arbitrary order D\(^\alpha ,\alpha \in \mathbf R_+ \cup \{0\}\). Application to ODEs and PDEs with entire and fractional derivatives
zbMATH Open document ID: 1186.46045
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-10-09T00:00:00Z
review text: The author introduces the extension of the Colombeau algebra of generalized functions to fractional derivatives. Further, this extension is applied to ODEs and PDEs having fractional derivatives of Dirac distributions with respect to temporal and spatial variables.
reviewed by: Adem Kilicman
Mathematics Subject Classification ID: 46F30
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35R99
zbMATH DE Number: 5612973
zbMATH Keywords: Colombeau algebra
zbMATH Keywords: fractional derivatives
zbMATH Keywords: dirac delta distributions
zbMATH Keywords: ODEs and PDEs driven by fractional derivatives
author: Mirjana Stojanović
MaRDI profile type: Publication
full work available at URL: j.na.2009.04.034
OpenAlex ID: W2082303875
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DOI: 10.1016/J.NA.2009.04.034
description: scientific article; zbMATH DE number 5612973