Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations
In this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact and approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant coefficients in a bounded domain with suitable initial c...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/5703916 |
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| _version_ | 1832568537805225984 |
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| author | Salah Abuasad Ishak Hashim Samsul Ariffin Abdul Karim |
| author_facet | Salah Abuasad Ishak Hashim Samsul Ariffin Abdul Karim |
| author_sort | Salah Abuasad |
| collection | DOAJ |
| description | In this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact and approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant coefficients in a bounded domain with suitable initial conditions. Different applications in two and three fractional order terms are given to illustrate our new modification. The approximate solutions are given in the form of series solutions. The results show that the m-FRDTM for MT-TFDEs is a powerful method and can be generalized to other types of multiterm time-fractional equations. |
| format | Article |
| id | doaj-art-f1b23e9aa4394219ba41f211a61131dc |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-f1b23e9aa4394219ba41f211a61131dc2025-02-03T00:58:56ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/57039165703916Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion EquationsSalah Abuasad0Ishak Hashim1Samsul Ariffin Abdul Karim2Preparatory Year Deanship, King Faisal University, 31982 Hofuf, Al-Hasa, Saudi ArabiaSchool of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM Bangi, 43600 Selangor, MalaysiaFundamental and Applied Sciences Department and Center for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 32610 Seri Iskandar, Perak DR, MalaysiaIn this study, we introduce a new modification of fractional reduced differential transform method (m-FRDTM) to find exact and approximate solutions for nonhomogeneous linear multiterm time-fractional diffusion equations (MT-TFDEs) of constant coefficients in a bounded domain with suitable initial conditions. Different applications in two and three fractional order terms are given to illustrate our new modification. The approximate solutions are given in the form of series solutions. The results show that the m-FRDTM for MT-TFDEs is a powerful method and can be generalized to other types of multiterm time-fractional equations.http://dx.doi.org/10.1155/2019/5703916 |
| spellingShingle | Salah Abuasad Ishak Hashim Samsul Ariffin Abdul Karim Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations Advances in Mathematical Physics |
| title | Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations |
| title_full | Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations |
| title_fullStr | Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations |
| title_full_unstemmed | Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations |
| title_short | Modified Fractional Reduced Differential Transform Method for the Solution of Multiterm Time-Fractional Diffusion Equations |
| title_sort | modified fractional reduced differential transform method for the solution of multiterm time fractional diffusion equations |
| url | http://dx.doi.org/10.1155/2019/5703916 |
| work_keys_str_mv | AT salahabuasad modifiedfractionalreduceddifferentialtransformmethodforthesolutionofmultitermtimefractionaldiffusionequations AT ishakhashim modifiedfractionalreduceddifferentialtransformmethodforthesolutionofmultitermtimefractionaldiffusionequations AT samsulariffinabdulkarim modifiedfractionalreduceddifferentialtransformmethodforthesolutionofmultitermtimefractionaldiffusionequations |