Convergence theorems for generalized viscosity explicit methods for nonexpansive mappings in banach spaces and some applications
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Author list: Sunthrayuth P., Pakkaranang N., Kumam P., Thounthong P., Cholamjiak P.
Publisher: MDPI
Publication year: 2019
Journal: Entropy (1099-4300)
Volume number: 7
Issue number: 2
ISSN: 1099-4300
eISSN: 1099-4300
Languages: English-Great Britain (EN-GB)
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Abstract
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. ฉ 2019 by the authors.
Keywords
Fractional-order of diffusion equations, Mittag-Leffler function
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