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
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.
ODEs and PDEs driven by fractional derivatives
scientific article; zbMATH DE number 5612973