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Entropy 2017, 19(7), 296; doi:10.3390/e19070296

Analytical Approximate Solutions of (n + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations

1
Department of Mathematics, Faculty of Art and Science, Siirt University, Siirt 56100, Turkey
2
Department of Mathematics, Faculty of Art and Sciences, Çankaya University, Ankara 06790, Turkey
3
Institute of Space Sciences, Magurele-Bucharest 077125, Romania
4
Department of Mathematics, Faculty of Art and Science, King Saud University, Riyadh 11495, Saudi Arabia
5
Department of Mathematics, Faculty of Science, Yuzuncu Yil University, Van 65080, Turkey
*
Author to whom correspondence should be addressed.
Received: 27 May 2017 / Revised: 15 June 2017 / Accepted: 20 June 2017 / Published: 22 June 2017
(This article belongs to the Special Issue Complex Systems and Fractional Dynamics)
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Abstract

In this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems. View Full-Text
Keywords: reduced differential transform method; heat like equation; wave like equation; fractional partial differential equations; local fractional derivative reduced differential transform method; heat like equation; wave like equation; fractional partial differential equations; local fractional derivative
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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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Acan, O.; Baleanu, D.; Qurashi, M.M.A.; Sakar, M.G. Analytical Approximate Solutions of (n + 1)-Dimensional Fractal Heat-Like and Wave-Like Equations. Entropy 2017, 19, 296.

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