Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator
This study investigates the Cauchy reaction-diffusion equation (CRDE) with the Atangana-Baleanu differential operator. The existence and uniqueness of solutions to fractional starting value issues are begun using the fixed-point theorem and contraction principle, respectively. The proposed study use...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S266681812400367X |
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| author | Hassan Kamil Jassim Ali Latif Arif |
| author_facet | Hassan Kamil Jassim Ali Latif Arif |
| author_sort | Hassan Kamil Jassim |
| collection | DOAJ |
| description | This study investigates the Cauchy reaction-diffusion equation (CRDE) with the Atangana-Baleanu differential operator. The existence and uniqueness of solutions to fractional starting value issues are begun using the fixed-point theorem and contraction principle, respectively. The proposed study uses the natural variation iteration technique (NVIM) to get an approximate solution for nonlinear fractional reaction-diffusion equations. This study's approximate answers are compared to other solutions found using known methodologies, and the results are discussed. The devised technique has benefits in terms of accuracy and computational cost efficiency, which may be used to solve nonlinear fractional reaction-diffusion equations. |
| format | Article |
| id | doaj-art-fa53ad650919458ebd26d60bb0bc3bdb |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-fa53ad650919458ebd26d60bb0bc3bdb2025-08-20T01:59:39ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-011210098110.1016/j.padiff.2024.100981Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operatorHassan Kamil Jassim0Ali Latif Arif1Corresponding author.; Department of Mathematics, College of Education for Pure Science, University of Thi-Qar, Thi-Qar, IraqDepartment of Mathematics, College of Education for Pure Science, University of Thi-Qar, Thi-Qar, IraqThis study investigates the Cauchy reaction-diffusion equation (CRDE) with the Atangana-Baleanu differential operator. The existence and uniqueness of solutions to fractional starting value issues are begun using the fixed-point theorem and contraction principle, respectively. The proposed study uses the natural variation iteration technique (NVIM) to get an approximate solution for nonlinear fractional reaction-diffusion equations. This study's approximate answers are compared to other solutions found using known methodologies, and the results are discussed. The devised technique has benefits in terms of accuracy and computational cost efficiency, which may be used to solve nonlinear fractional reaction-diffusion equations.http://www.sciencedirect.com/science/article/pii/S266681812400367XCauchy reaction-diffusion equationsNatural transformVariation iteration method |
| spellingShingle | Hassan Kamil Jassim Ali Latif Arif Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator Partial Differential Equations in Applied Mathematics Cauchy reaction-diffusion equations Natural transform Variation iteration method |
| title | Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator |
| title_full | Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator |
| title_fullStr | Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator |
| title_full_unstemmed | Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator |
| title_short | Analysis of Cauchy reaction-diffusion equations involving Atangana-Baleanu fractional operator |
| title_sort | analysis of cauchy reaction diffusion equations involving atangana baleanu fractional operator |
| topic | Cauchy reaction-diffusion equations Natural transform Variation iteration method |
| url | http://www.sciencedirect.com/science/article/pii/S266681812400367X |
| work_keys_str_mv | AT hassankamiljassim analysisofcauchyreactiondiffusionequationsinvolvingatanganabaleanufractionaloperator AT alilatifarif analysisofcauchyreactiondiffusionequationsinvolvingatanganabaleanufractionaloperator |