Properties of the Katugampola fractional derivative with potential application in quantum mechanics
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Publication:5264382
DOI10.1063/1.4922018zbMath1323.26008OpenAlexW566301135MaRDI QIDQ5264382
Douglas R. Anderson, Darin J. Ulness
Publication date: 27 July 2015
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/47dff09f46abbcf491655d4d600a33018e86208a
Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Fractional derivatives and integrals (26A33) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Mellin transforms of generalized fractional integrals and derivatives
- Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods
- On conformable fractional calculus
- Fractional variational calculus with classical and combined Caputo derivatives
- Recent history of fractional calculus
- Fractional quantum mechanics and Lévy path integrals
- A new definition of fractional derivative
- On the numerical solution of the eigenvalue problem in fractional quantum mechanics
- Advanced methods in the fractional calculus of variations
- REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELS
- Principles of Fractional Quantum Mechanics
- The power quantum calculus and variational problems
- On the nonlocality of the fractional Schrödinger equation
- A New Approach to Generalized Fractional Derivatives
- Fractional Schrödinger equation for a particle moving in a potential well
- Quantum Variational Calculus
- Preface
- Dynamics of the fractional oscillator
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