![]() Asian Academic Publisher, Hong Kong 2011. Yang XJ: Local Fractional Functional Analysis and Its Applications. Yang XJ: Local fractional integral transforms. 10.1006/jmaa.2001.7656īalankin AS, Elizarraraz BE: Map of fluid flow in fractal porous medium into fractal continuum flow. Parvate A, Gangal AD: Calculus on fractal subsets of real line - I: formulation. Jumarie G: Table of some basic fractional calculus formulae derived from a modified Riemann-Liouville derivative for non-differentiable functions. Kolwankar KM, Gangal AD: Fractional differentiability of nowhere differentiable functions and dimensions. ![]() Kong HY, He JH: The fractal harmonic law and its application to swimming suit. (2007) arXiv:0709.0898Ĭaruso F, Oguri V: The cosmic microwave background spectrum and an upper limit for fractal space dimensionality. ![]() Maziashvili, M: Space-time uncertainty relation and operational definition of dimension. Saleh AA: On the dimension of micro space-time. Nottale L: Fractals and the quantum theory of space-time. Zeilinger A, Svozil K: Measuring the dimension of space-time. Freeman, New York 1982.įalconer KJ: Fractal Geometry-Mathematical Foundations and Application. Mandelbrot BB: The Fractal Geometry of Nature. Finally, the conclusions are presented in Section 6. Application of quantum mechanics in fractal space is considered in Section 5. The Heisenberg uncertainty principle in local fractional Fourier analysis is studied in Section 4. The theory of local fractional Fourier analysis is introduced in Section 3. In Section 2, the preliminary results for the local fractional calculus are investigated. The main purpose of this paper is to present the mathematical aspects of the Heisenberg uncertainty principle within local fractional Fourier analysis and to structure a local fractional version of the Schrödinger equation. ![]() ![]() Also, its applications were investigated in quantum mechanics, differentials equations and signals. The theory of local fractional Fourier analysis is structured in a generalized Hilbert space (fractal space), and some results were obtained. Local fractional Fourier analysis, which is a generalization of the Fourier analysis in fractal space, has played an important role in handling non-differentiable functions. The fractional Heisenberg uncertainty principle and the fractional Schrödinger equation based on fractional Fourier analysis were proposed. This formalism was applied in describing physical phenomena such as continuum mechanics, elasticity, quantum mechanics, heat-diffusion and wave phenomena, and other branches of applied mathematics and nonlinear dynamics. The theory of local fractional calculus, started to be considered as one of the useful tools to handle the fractal and continuously non-differentiable functions. As it is known, the fractal curves are everywhere continuous but nowhere differentiable therefore, we cannot use the classical calculus to describe the motions in Cantor time-space. ![]()
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