A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique
This paper presents a novel semi-analytical approach to solve 2D fuzzy fractional heat equation which combines Shehu transform with Homotopy Perturbation Method. This method efficiently generates dual-bound solutions (lower and upper bounds) that precisely capture uncertainty inherent in fuzzy fract...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001342 |
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| author | Mamta Kapoor |
| author_facet | Mamta Kapoor |
| author_sort | Mamta Kapoor |
| collection | DOAJ |
| description | This paper presents a novel semi-analytical approach to solve 2D fuzzy fractional heat equation which combines Shehu transform with Homotopy Perturbation Method. This method efficiently generates dual-bound solutions (lower and upper bounds) that precisely capture uncertainty inherent in fuzzy fractional systems. Proposed technique demonstrates remarkable advantages: it effectively handles the complexity of fractional derivatives while maintaining computational efficiency compared to traditional numerical methods. Through rigorous validation via using three distinct test illustrations, method’s accuracy and reliability are confirmed through comprehensive graphical and tabular analyses. The results disclose excellent agreement between approximate solutions and benchmark solutions, with confirmed theoretical and numerical convergence. Notably, this approach proves particularly valuable to handle problems where exact analytical solutions are unavailable or computationally difficult to fetch. This work not only provides a robust framework to solve fuzzy fractional PDEs but also offers practical insights for applications in heat transfer, diffusion processes, and other engineering systems involving uncertainty and memory effects. The method's efficiency and accuracy make it a compelling alternative to conventional numerical schemes for complex differential equations. |
| format | Article |
| id | doaj-art-b50012d9df6b48e9b35be68e0ae93d18 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-b50012d9df6b48e9b35be68e0ae93d182025-08-20T03:48:51ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410120710.1016/j.padiff.2025.101207A robust study upon fuzzy fractional 2D heat equation via semi-analytical techniqueMamta Kapoor0Marwadi University Research Center, Department of Mathematics, Faculty of Engineering & Technology, Marwadi University, Rajkot, 360003, Gujarat, IndiaThis paper presents a novel semi-analytical approach to solve 2D fuzzy fractional heat equation which combines Shehu transform with Homotopy Perturbation Method. This method efficiently generates dual-bound solutions (lower and upper bounds) that precisely capture uncertainty inherent in fuzzy fractional systems. Proposed technique demonstrates remarkable advantages: it effectively handles the complexity of fractional derivatives while maintaining computational efficiency compared to traditional numerical methods. Through rigorous validation via using three distinct test illustrations, method’s accuracy and reliability are confirmed through comprehensive graphical and tabular analyses. The results disclose excellent agreement between approximate solutions and benchmark solutions, with confirmed theoretical and numerical convergence. Notably, this approach proves particularly valuable to handle problems where exact analytical solutions are unavailable or computationally difficult to fetch. This work not only provides a robust framework to solve fuzzy fractional PDEs but also offers practical insights for applications in heat transfer, diffusion processes, and other engineering systems involving uncertainty and memory effects. The method's efficiency and accuracy make it a compelling alternative to conventional numerical schemes for complex differential equations.http://www.sciencedirect.com/science/article/pii/S2666818125001342Shehu transformHomotopy perturbation methodFuzzy fractional Heat equation |
| spellingShingle | Mamta Kapoor A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique Partial Differential Equations in Applied Mathematics Shehu transform Homotopy perturbation method Fuzzy fractional Heat equation |
| title | A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique |
| title_full | A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique |
| title_fullStr | A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique |
| title_full_unstemmed | A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique |
| title_short | A robust study upon fuzzy fractional 2D heat equation via semi-analytical technique |
| title_sort | robust study upon fuzzy fractional 2d heat equation via semi analytical technique |
| topic | Shehu transform Homotopy perturbation method Fuzzy fractional Heat equation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001342 |
| work_keys_str_mv | AT mamtakapoor arobuststudyuponfuzzyfractional2dheatequationviasemianalyticaltechnique AT mamtakapoor robuststudyuponfuzzyfractional2dheatequationviasemianalyticaltechnique |