On the Exact Solution of Wave Equations on Cantor Sets

Entropy

Dumitru Baleanu²  Hasib Khan³  Hossien Jafari¹  Rahmat Ali Khan³ 

[1] Department of Mathematical Sciences, University of South Africa, P. O. Box 392, UNISA 0003, South Africa; E-Mail:;Department of Mathematics Computer Science, Cankaya University, Ankara 06530, Turkey;University of Malakand, Chakdara, Dir lower, P. O. Box, Khybar Pakhtunkhwa 18000, Pakistan

关键词: local fractional calculus;    local fractional Laplace variation iteration method;    local fractional wave equations;   

DOI  :  10.3390/e17096229

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.