Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method
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 th...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-06-01
|
| Series: | Entropy |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1099-4300/21/6/557 |
| _version_ | 1811299524822433792 |
|---|---|
| author | Rasool Shah Hassan Khan Saima Mustafa Poom Kumam Muhammad Arif |
| author_facet | Rasool Shah Hassan Khan Saima Mustafa Poom Kumam Muhammad Arif |
| author_sort | Rasool Shah |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T06:37:05Z |
| format | Article |
| id | doaj.art-0a5be43c8c6649e9accbddde73b2a5cb |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-13T06:37:05Z |
| publishDate | 2019-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0a5be43c8c6649e9accbddde73b2a5cb2022-12-22T02:57:51ZengMDPI AGEntropy1099-43002019-06-0121655710.3390/e21060557e21060557Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition MethodRasool Shah0Hassan Khan1Saima Mustafa2Poom Kumam3Muhammad Arif4Department of Mathematics, Abdul Wali khan University, Mardan 23200, PakistanDepartment of Mathematics, Abdul Wali khan University, Mardan 23200, PakistanDepartment of Mathematics, Pir Mehr Ali Shah Arid Agriculture University, Rawalpindi 46000, PakistanCenter 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, ThailandDepartment of Mathematics, Abdul Wali khan University, Mardan 23200, PakistanIn 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.https://www.mdpi.com/1099-4300/21/6/557Natural transform decomposition methodfractional-order of diffusion equationsMittag–Leffler function |
| spellingShingle | Rasool Shah Hassan Khan Saima Mustafa Poom Kumam Muhammad Arif Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method Entropy Natural transform decomposition method fractional-order of diffusion equations Mittag–Leffler function |
| title | Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method |
| title_full | Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method |
| title_fullStr | Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method |
| title_full_unstemmed | Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method |
| title_short | Analytical Solutions of Fractional-Order Diffusion Equations by Natural Transform Decomposition Method |
| title_sort | analytical solutions of fractional order diffusion equations by natural transform decomposition method |
| topic | Natural transform decomposition method fractional-order of diffusion equations Mittag–Leffler function |
| url | https://www.mdpi.com/1099-4300/21/6/557 |
| work_keys_str_mv | AT rasoolshah analyticalsolutionsoffractionalorderdiffusionequationsbynaturaltransformdecompositionmethod AT hassankhan analyticalsolutionsoffractionalorderdiffusionequationsbynaturaltransformdecompositionmethod AT saimamustafa analyticalsolutionsoffractionalorderdiffusionequationsbynaturaltransformdecompositionmethod AT poomkumam analyticalsolutionsoffractionalorderdiffusionequationsbynaturaltransformdecompositionmethod AT muhammadarif analyticalsolutionsoffractionalorderdiffusionequationsbynaturaltransformdecompositionmethod |