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Entropy 2015, 17(9), 6229-6237; doi:10.3390/e17096229

On the Exact Solution of Wave Equations on Cantor Sets

1,2,†,* , 3,4,†, 5,6,†
and
3,†
1
Department of Mathematics Computer Science, Cankaya University, Ankara 06530, Turkey
2
Institute of Space Sciences, P. O. Box, MG-23, Magurele-Bucharest 76900, Romania
3
University of Malakand, Chakdara, Dir lower, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan
4
Shaheed Benazir Bhutto University, Sheringal, Dir Upper, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan
5
Department of Mathematical Sciences, University of South Africa, P. O. Box 392, UNISA 0003, South Africa
6
Department of Mathematical Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Raúl Alcaraz Martínez
Received: 28 June 2015 / Revised: 1 August 2015 / Accepted: 6 August 2015 / Published: 8 September 2015
(This article belongs to the Special Issue Wavelets, Fractals and Information Theory)
View Full-Text   |   Download PDF [612 KB, uploaded 8 September 2015]   |  

Abstract

The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM). We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs). The efficiency of the scheme is examined by two illustrative examples. View Full-Text
Keywords: local fractional calculus; local fractional Laplace variation iteration method; local fractional wave equations local fractional calculus; local fractional Laplace variation iteration method; local fractional wave equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Baleanu, D.; Khan, H.; Jafari, H.; Khan, R.A. On the Exact Solution of Wave Equations on Cantor Sets. Entropy 2015, 17, 6229-6237.

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