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

DOI10.1016/j.na.2009.04.034zbMath1186.46045OpenAlexW2082303875MaRDI QIDQ732578

Mirjana Stojanovic

Publication date: 9 October 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.04.034

zbMATH Keywords

fractional derivativesColombeau algebradirac delta distributionsODEs and PDEs driven by fractional derivatives

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Miscellaneous topics in partial differential equations (35R99) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (5)

FOUNDATION OF THE FRACTIONAL CALCULUS IN GENERALIZED FUNCTION ALGEBRAS ⋮ Solving the fractional Schrödinger equation with singular initial data in the extended Colombeau algebra of generalized functions ⋮ Generalized Solution of Transport Equation ⋮ Calculus of variations and optimal control for generalized functions ⋮ Unnamed Item

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• Fractional Calculus: Integral and Differential Equations of Fractional Order
• Ordinary differential equations with delta function terms

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