Local fractional Fourier analysis, Advances in Mechanical Engineering and its Applications, 1(1) (2012)12-16
Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series.
http://www.worldsciencepublisher.org/journals/index.php/AMEA/article/view/264
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