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 (Q732578)
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scientific article; zbMATH DE number 5612973
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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 |
scientific article; zbMATH DE number 5612973 |
Statements
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 (English)
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9 October 2009
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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.
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Colombeau algebra
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fractional derivatives
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dirac delta distributions
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ODEs and PDEs driven by fractional derivatives
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