Neural Networks-Based Analytical Solver for Exact Solutions of Fractional Partial Differential Equations Article Swipe
Shanhao Yuan
,
Yanqin Liu
,
Limei Yan
,
Runfa Zhang
,
Shunjun Wu
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9080541
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3390/fractalfract9080541
This paper introduces an innovative artificial neural networks-based analytical solver for fractional partial differential equations (fPDEs), combining neural networks (NNs) with symbolic computation. Leveraging the powerful function approximation ability of NNs and the exactness of symbolic methods, our approach achieves notable improvements in both computational speed and solution precision. The efficacy of the proposed method is validated through four numerical examples, with results visualized using three-dimensional surface plots, contour mappings, and density distributions. Numerical experiments demonstrate that the proposed framework successfully derives exact solutions for fPDEs without relying on data samples. This research provides a novel methodological framework for solving fPDEs, with broad applicability across scientific and engineering fields.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3390/fractalfract9080541
- https://www.mdpi.com/2504-3110/9/8/541/pdf?version=1755509198
- OA Status
- gold
- Cited By
- 1
- References
- 44
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4413279245
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Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4413279245Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3390/fractalfract9080541Digital Object Identifier
- Title
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Neural Networks-Based Analytical Solver for Exact Solutions of Fractional Partial Differential EquationsWork title
- Type
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articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2025Year of publication
- Publication date
-
2025-08-16Full publication date if available
- Authors
-
Shanhao Yuan, Yanqin Liu, Limei Yan, Runfa Zhang, Shunjun WuList of authors in order
- Landing page
-
https://doi.org/10.3390/fractalfract9080541Publisher landing page
- PDF URL
-
https://www.mdpi.com/2504-3110/9/8/541/pdf?version=1755509198Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
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goldOpen access status per OpenAlex
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https://www.mdpi.com/2504-3110/9/8/541/pdf?version=1755509198Direct OA link when available
- Concepts
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Solver, Partial differential equation, Applied mathematics, Fractional calculus, Mathematics, Mathematical analysis, Computer science, Mathematical optimizationTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
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2025: 1Per-year citation counts (last 5 years)
- References (count)
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44Number of works referenced by this work
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| referenced_works | https://openalex.org/W4360979997, https://openalex.org/W2605056791, https://openalex.org/W4390490482, https://openalex.org/W4387673543, https://openalex.org/W4229442868, https://openalex.org/W4391264960, https://openalex.org/W3000047757, https://openalex.org/W4390812655, https://openalex.org/W4386688311, https://openalex.org/W4390729286, https://openalex.org/W6873149515, https://openalex.org/W4400874172, https://openalex.org/W4391785281, https://openalex.org/W4387339080, https://openalex.org/W4324092247, https://openalex.org/W6868090607, https://openalex.org/W3208687975, https://openalex.org/W4391765461, https://openalex.org/W4394693586, https://openalex.org/W4382448966, https://openalex.org/W2097021318, https://openalex.org/W4392014361, https://openalex.org/W4398206937, https://openalex.org/W3014009018, https://openalex.org/W2899283552, https://openalex.org/W4220717841, https://openalex.org/W6867078177, https://openalex.org/W2969381807, https://openalex.org/W4292440370, https://openalex.org/W4387613886, https://openalex.org/W4402964355, https://openalex.org/W4400640382, https://openalex.org/W4327571592, https://openalex.org/W6792006057, https://openalex.org/W4317938533, https://openalex.org/W4200218775, https://openalex.org/W1989317524, https://openalex.org/W2006773431, https://openalex.org/W2067577527, https://openalex.org/W2907294897, https://openalex.org/W4398161968, https://openalex.org/W4396799269, https://openalex.org/W4403460989, https://openalex.org/W3138137334 |
| referenced_works_count | 44 |
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