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Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method

1
Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
2
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(6), 597; https://doi.org/10.3390/e21060597
Received: 29 April 2019 / Revised: 1 June 2019 / Accepted: 4 June 2019 / Published: 16 June 2019
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Abstract

In the present article, fractional-order heat and wave equations are solved by using the natural transform decomposition method. The series form solutions are obtained for fractional-order heat and wave equations, using the proposed method. Some numerical examples are presented to understand the procedure of natural transform decomposition method. The natural transform decomposition method procedure has shown that less volume of calculations and a high rate of convergence can be easily applied to other nonlinear problems. Therefore, the natural transform decomposition method is considered to be one of the best analytical techniques, in order to solve fractional-order linear and nonlinear Partial deferential equations, particularly fractional-order heat and wave equation. View Full-Text
Keywords: natural transform decomposition method; fractional-order heat and wave equations; Caputo operator natural transform decomposition method; fractional-order heat and wave equations; Caputo operator
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Khan, H.; Shah, R.; Kumam, P.; Arif, M. Analytical Solutions of Fractional-Order Heat and Wave Equations by the Natural Transform Decomposition Method. Entropy 2019, 21, 597.

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