Properties of the Katugampola fractional derivative with potential application in quantum mechanics
- 1 June 2015
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 56 (6), 063502
- https://doi.org/10.1063/1.4922018
Abstract
Katugampola [e-print arXiv:1410.6535] recently introduced a limit based fractional derivative, Dα (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, , and the associated differential operator, Dα = t1−αD1. 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.
This publication has 21 references indexed in Scilit:
- On conformable fractional calculusJournal of Computational and Applied Mathematics, 2015
- Mellin transforms of generalized fractional integrals and derivativesApplied Mathematics and Computation, 2015
- Advanced Methods in the Fractional Calculus of VariationsPublished by Springer Science and Business Media LLC ,2015
- Colloquium: Fractional calculus view of complexity: A tutorialReviews of Modern Physics, 2014
- A new definition of fractional derivativeJournal of Computational and Applied Mathematics, 2014
- Quantum Variational CalculusPublished by Springer Science and Business Media LLC ,2014
- REVIEW OF SOME PROMISING FRACTIONAL PHYSICAL MODELSInternational Journal of Modern Physics B, 2013
- Fractional variational calculus with classical and combined Caputo derivativesNonlinear Analysis, 2012
- Recent history of fractional calculusCommunications in Nonlinear Science and Numerical Simulation, 2011
- Fractional CalculusPublished by World Scientific Pub Co Pte Ltd ,2011