Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach
The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/9945364 |
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| _version_ | 1832559742513315840 |
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| author | Nehad Ali Shah S. Saleem Ali Akgül Kamsing Nonlaopon Jae Dong Chung |
| author_facet | Nehad Ali Shah S. Saleem Ali Akgül Kamsing Nonlaopon Jae Dong Chung |
| author_sort | Nehad Ali Shah |
| collection | DOAJ |
| description | The aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems. |
| format | Article |
| id | doaj-art-1091d49eaa244a41b2d0d491291b36b6 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-1091d49eaa244a41b2d0d491291b36b62025-02-03T01:29:19ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/99453649945364Numerical Analysis of Time-Fractional Diffusion Equations via a Novel ApproachNehad Ali Shah0S. Saleem1Ali Akgül2Kamsing Nonlaopon3Jae Dong Chung4Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of KoreaDepartment of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi ArabiaSiirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, TurkeyDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, ThailandDepartment of Mechanical Engineering, Sejong University, Seoul 05006, Republic of KoreaThe aim of this paper is a new semianalytical technique called the variational iteration transform method for solving fractional-order diffusion equations. In the variational iteration technique, identifying of the Lagrange multiplier is an essential rule, and variational theory is commonly used for this purpose. The current technique has the edge over other methods as it does not need extra parameters and polynomials. The validity of the proposed method is verified by considering some numerical problems. The solution achieved has shown that the better accuracy of the proposed technique. This paper proposes a simpler method to calculate the multiplier using the Shehu transformation, making a valuable technique to researchers dealing with various linear and nonlinear problems.http://dx.doi.org/10.1155/2021/9945364 |
| spellingShingle | Nehad Ali Shah S. Saleem Ali Akgül Kamsing Nonlaopon Jae Dong Chung Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach Journal of Function Spaces |
| title | Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach |
| title_full | Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach |
| title_fullStr | Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach |
| title_full_unstemmed | Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach |
| title_short | Numerical Analysis of Time-Fractional Diffusion Equations via a Novel Approach |
| title_sort | numerical analysis of time fractional diffusion equations via a novel approach |
| url | http://dx.doi.org/10.1155/2021/9945364 |
| work_keys_str_mv | AT nehadalishah numericalanalysisoftimefractionaldiffusionequationsviaanovelapproach AT ssaleem numericalanalysisoftimefractionaldiffusionequationsviaanovelapproach AT aliakgul numericalanalysisoftimefractionaldiffusionequationsviaanovelapproach AT kamsingnonlaopon numericalanalysisoftimefractionaldiffusionequationsviaanovelapproach AT jaedongchung numericalanalysisoftimefractionaldiffusionequationsviaanovelapproach |