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**Local fractional Fourier series with application to wave equation in fractal vibrating string.**
*(English)*
Zbl 1257.35193

Summary: We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

### MSC:

35R11 | Fractional partial differential equations |

33E12 | Mittag-Leffler functions and generalizations |

81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |

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\textit{M.-S. Hu} et al., Abstr. Appl. Anal. 2012, Article ID 567401, 15 p. (2012; Zbl 1257.35193)

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