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Open AccessArticle

# Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method

by 3,4,* and
1
Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
2
Department of Mathematics, Pir Mehr Ali Shah Arid Agriculture University, Rawalpindi 46000, Pakistan
3
Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
4
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), 557; https://doi.org/10.3390/e21060557
Received: 15 April 2019 / Revised: 5 May 2019 / Accepted: 7 May 2019 / Published: 3 June 2019
(This article belongs to the Special Issue The Fractional View of Complexity)
In the present article, fractional-order diffusion equations are solved using the Natural transform decomposition method. The series form solutions are obtained for fractional-order diffusion equations using the proposed method. Some numerical examples are presented to understand the procedure of the Natural transform decomposition method. The Natural transform decomposition method has shown the least volume of calculations and a high rate of convergence compared to other analytical techniques, the proposed method can also be easily applied to other non-linear problems. Therefore, the Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear partial deferential equations, particularly fractional-order diffusion equation. View Full-Text
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Shah, R.; Khan, H.; Mustafa, S.; Kumam, P.; Arif, M. Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method. Entropy 2019, 21, 557.