Solving the Fractional Schrödinger Equation with Singular Initial Data in the Extended Colombeau Algebra of Generalized Functions
Copyright policy )Solving the Fractional Schrödinger Equation with Singular Initial Data in the Extended Colombeau Algebra of Generalized Functions
This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. 1 / ı ∂ / ∂ t u t , x − △ u t , x + v x u t , x = 0 , t ∈ R + , x ∈ R n , v x = δ x , u 0 , x = δ x , where δ is the Dirac distribution. The proofs of our main results are based on the Gronwall inequality and regularization method. We conclude our article by establishing the association concept of solutions.
- Université Sultan Moulay Slimane Morocco
Dirac initial function, Colombeau Algebras, Crystallography, Time-Fractional Diffusion Equation, Applied Mathematics, Physics, Applications of Generalized Functions in Mathematics and Physics, Stability of Functional Equations in Mathematical Analysis, Fractional partial differential equations, Fractional Derivatives, Chemistry, Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.), Generalized Functions, Modeling and Simulation, Time-dependent Schrödinger equations and Dirac equations, Physical Sciences, QA1-939, FOS: Mathematics, Fractional Calculus, regularization method, Mathematical Physics, Mathematics, Anomalous Diffusion Modeling and Analysis
Dirac initial function, Colombeau Algebras, Crystallography, Time-Fractional Diffusion Equation, Applied Mathematics, Physics, Applications of Generalized Functions in Mathematics and Physics, Stability of Functional Equations in Mathematical Analysis, Fractional partial differential equations, Fractional Derivatives, Chemistry, Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.), Generalized Functions, Modeling and Simulation, Time-dependent Schrödinger equations and Dirac equations, Physical Sciences, QA1-939, FOS: Mathematics, Fractional Calculus, regularization method, Mathematical Physics, Mathematics, Anomalous Diffusion Modeling and Analysis
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!