Solving the fractional Schrödinger equation with singular initial data in the extended Colombeau algebra of generalized functions

DOI10.1155/2023/3493912zbMath1518.35627OpenAlexW4367676374MaRDI QIDQ6101430

Said Melliani, Abdellah Taqbibt, Mhamed Elomari, Ali El Mfadel

Publication date: 20 June 2023

Published in: International Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2023/3493912

zbMATH Keywords

regularization methodDirac initial function

Mathematics Subject Classification ID

Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

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• 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
• Théorie des distributions à valeurs vectorielles
• The fractional Schrödinger equation with general nonnegative potentials. The weighted space approach
• On impulsive boundary value problem with Riemann-Liouville fractional order derivative
• Nonlinear Schrödinger equation with singular potential and initial data
• FOUNDATION OF THE FRACTIONAL CALCULUS IN GENERALIZED FUNCTION ALGEBRAS

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