Next Article in Journal
Statistical Complexity of the Coriolis Antipairing Effect
Next Article in Special Issue
An Entropy Formulation Based on the Generalized Liouville Fractional Derivative
Previous Article in Journal
Offshore Platform Extraction Using RadarSat-2 SAR Imagery: A Two-Parameter CFAR Method Based on Maximum Entropy
Previous Article in Special Issue
Complexity Analysis of Escher’s Art
Open AccessArticle

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

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
Keywords: Natural transform decomposition method; fractional-order of diffusion equations; Mittag–Leffler function Natural transform decomposition method; fractional-order of diffusion equations; Mittag–Leffler function
Show Figures

Figure 1

MDPI and ACS Style

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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop