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Title: Properties of the Katugampola fractional derivative with potential application in quantum mechanics

Katugampola [e-print http://arxiv.org/abs/1410.6535 ] recently introduced a limit based fractional derivative, D{sup α} (referred to in this work as the Katugampola fractional derivative) that maintains many of the familiar properties of standard derivatives such as the product, quotient, and chain rules. Typically, fractional derivatives are handled using an integral representation and, as such, are non-local in character. The current work starts with a key property of the Katugampola fractional derivative, D{sup α}[y]=t{sup 1−α}(dy)/(dt) , and the associated differential operator, D{sup α} = t{sup 1−α}D{sup 1}. These operators, their inverses, commutators, anti-commutators, and several important differential equations are studied. The anti-commutator serves as a basis for the development of a self-adjoint operator which could potentially be useful in quantum mechanics. A Hamiltonian is constructed from this operator and applied to the particle in a box model.
Authors:
 [1] ;  [2]
  1. Department of Mathematics, Concordia College, Moorhead, Minnesota 56562 (United States)
  2. Department of Chemistry, Concordia College, Moorhead, Minnesota 56562 (United States)
Publication Date:
OSTI Identifier:
22403158
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOX MODELS; COMMUTATORS; DIFFERENTIAL EQUATIONS; HAMILTONIANS; INTEGRALS; PARTICLES; POTENTIALS; QUANTUM MECHANICS