Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model
This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named <i>q</i>-HATM (<i>q</i>-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model an...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/12/1976 |
| _version_ | 1797546256280584192 |
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| author | Cyril D. Enyi |
| author_facet | Cyril D. Enyi |
| author_sort | Cyril D. Enyi |
| collection | DOAJ |
| description | This paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named <i>q</i>-HATM (<i>q</i>-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating from biological sciences. The overwhelming agreement of our analytical solution by the <i>q</i>-HATM technique with the exact solution indeed establishes the efficacy of <i>q</i>-HATM to solve the fractional Fornberg–Whitham model and the two-dimensional fractional population model. Furthermore, comparisons by means of extensive analysis using numerics, graphs and error analysis are presented to affirm the preference of <i>q</i>-HATM technique over other methods. A variant of the <i>q</i>-HATM using symmetry can also be considered to solve these problems. |
| first_indexed | 2024-03-10T14:27:27Z |
| format | Article |
| id | doaj.art-b73bc972753d41e29654751a348beb1c |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T14:27:27Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b73bc972753d41e29654751a348beb1c2023-11-20T22:54:20ZengMDPI AGSymmetry2073-89942020-11-011212197610.3390/sym12121976Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population ModelCyril D. Enyi0Department of Mathematics, University of Hafr Al Batin, Hafar Al Batin 39524, Saudi ArabiaThis paper presents an efficacious analytical and numerical method for solution of fractional differential equations. This technique, here in named <i>q</i>-HATM (<i>q</i>-homotopy analysis transform method) is applied to a one-dimensional fractional Fornberg–Whitham model and a two-dimensional fractional population model emanating from biological sciences. The overwhelming agreement of our analytical solution by the <i>q</i>-HATM technique with the exact solution indeed establishes the efficacy of <i>q</i>-HATM to solve the fractional Fornberg–Whitham model and the two-dimensional fractional population model. Furthermore, comparisons by means of extensive analysis using numerics, graphs and error analysis are presented to affirm the preference of <i>q</i>-HATM technique over other methods. A variant of the <i>q</i>-HATM using symmetry can also be considered to solve these problems.https://www.mdpi.com/2073-8994/12/12/1976Laplace transform<i>q</i>-homotopy analysis transform methodFornberg–Whitham equationfractional biological population modelsymmetry |
| spellingShingle | Cyril D. Enyi Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model Symmetry Laplace transform <i>q</i>-homotopy analysis transform method Fornberg–Whitham equation fractional biological population model symmetry |
| title | Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model |
| title_full | Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model |
| title_fullStr | Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model |
| title_full_unstemmed | Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model |
| title_short | Efficacious Analytical Technique Applied to Fractional Fornberg–Whitham Model and Two-Dimensional Fractional Population Model |
| title_sort | efficacious analytical technique applied to fractional fornberg whitham model and two dimensional fractional population model |
| topic | Laplace transform <i>q</i>-homotopy analysis transform method Fornberg–Whitham equation fractional biological population model symmetry |
| url | https://www.mdpi.com/2073-8994/12/12/1976 |
| work_keys_str_mv | AT cyrildenyi efficaciousanalyticaltechniqueappliedtofractionalfornbergwhithammodelandtwodimensionalfractionalpopulationmodel |