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Open Access Research

Mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis

Xiao-Jun Yang123*, Dumitru Baleanu456 and José António Tenreiro Machado7

Author Affiliations

1 Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu, 221008, China

2 Institute of Software Science, Zhengzhou Normal University, Zhengzhou, 450044, China

3 Institute of Applied Mathematics, Qujing Normal University, Qujing, 655011, China

4 Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Cankaya University, Ankara, 06530, Turkey

5 Institute of Space Sciences, Magurele, Bucharest, Romania

6 Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, 21589, Saudi Arabia

7 Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida, 431, Porto, 4200-072, Portugal

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Boundary Value Problems 2013, 2013:131  doi:10.1186/1687-2770-2013-131

Published: 20 May 2013

Abstract

In this paper, we discuss the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis. The Schrödinger equation and Heisenberg uncertainty principles are structured within local fractional operators.

Keywords:
Heisenberg uncertainty principle; local fractional Fourier operator; Schrödinger equation; fractal time-space