A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation
Abstract This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear diffe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-03-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-023-01795-2 |
| _version_ | 1797247148530597888 |
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| author | Umut Bektaş Halil Anaç |
| author_facet | Umut Bektaş Halil Anaç |
| author_sort | Umut Bektaş |
| collection | DOAJ |
| description | Abstract This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table. |
| first_indexed | 2024-04-24T19:54:05Z |
| format | Article |
| id | doaj.art-a4aa251b6511417484bbdb7372c5c515 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-04-24T19:54:05Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-a4aa251b6511417484bbdb7372c5c5152024-03-24T12:28:00ZengSpringerOpenBoundary Value Problems1687-27702024-03-012024111310.1186/s13661-023-01795-2A hybrid method to solve a fractional-order Newell–Whitehead–Segel equationUmut Bektaş0Halil Anaç1Graduate Education Institute, Gümüşhane UniversityTorul Vocational School, Gümüşhane UniversityAbstract This paper solves fractional differential equations using the Shehu transform in combination with the q-homotopy analysis transform method (q-HATM). As the Shehu transform is only applicable to linear equations, q-HATM is an efficient technique for approximating solutions to nonlinear differential equations. In nonlinear systems that explain the emergence of stripes in 2D systems, the Newell–Whitehead–Segel equation plays a significant role. The findings indicate that the outcomes derived from the tables yield superior results compared to the existing LTDM in the literature. Maple is utilized to depict three-dimensional surfaces and find numerical values that are displayed in a table.https://doi.org/10.1186/s13661-023-01795-2Fractional differential equationNewell–Whitehead–Segel equationq-homotopy Shehu analysis transform methodShehu transform |
| spellingShingle | Umut Bektaş Halil Anaç A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation Boundary Value Problems Fractional differential equation Newell–Whitehead–Segel equation q-homotopy Shehu analysis transform method Shehu transform |
| title | A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation |
| title_full | A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation |
| title_fullStr | A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation |
| title_full_unstemmed | A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation |
| title_short | A hybrid method to solve a fractional-order Newell–Whitehead–Segel equation |
| title_sort | hybrid method to solve a fractional order newell whitehead segel equation |
| topic | Fractional differential equation Newell–Whitehead–Segel equation q-homotopy Shehu analysis transform method Shehu transform |
| url | https://doi.org/10.1186/s13661-023-01795-2 |
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