Algorithms and applications of the new modified decomposition method to solve initial-boundary value problems for fractional partial differential equations
This study aims to efficiently solve the class of initial-boundary problems for fractional partial differential equations by expanding the modified Adomian decomposition method. Three new algorithms are proposed, two for handling various fractional initial-boundary problems via the $ x $-differentia...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2025-03-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025267 |
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| Summary: | This study aims to efficiently solve the class of initial-boundary problems for fractional partial differential equations by expanding the modified Adomian decomposition method. Three new algorithms are proposed, two for handling various fractional initial-boundary problems via the $ x $-differential operator, and one for using the $ t $-differential operator. The proposed methods are designed to increase computational efficiency and ensure greater accuracy in the solutions. The effectiveness of the techniques is reviewed by applying them to a variety of cases, demonstrating their ability to address a broad range of fractional calculus problems. The results emphasize the flexibility and adaptability of the developed algorithms as reliable methods. |
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| ISSN: | 2473-6988 |