Spectral algorithm for fractional BVPs via novel modified Chebyshev polynomials fractional derivatives Article Swipe
Mohamed Abdelhakem
,
Dina Abdelhamied
,
Mamdouh El-kady
,
Youssri Hassan Youssri
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3846/mma.2025.22745
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.3846/mma.2025.22745
This paper introduces a spectral algorithm tailored for solving fractional boundary value problems (BVPs) using the fractional derivatives of modified Chebyshev polynomials. Specifically, it addresses linear and non-linear BVPs and Bratu equations in one dimension via spectral methods. The approach employs basis functions derived from first-kind shifted polynomials that satisfy the homogeneous boundary conditions. The fractional derivatives are formulated to facilitate the solution process. The convergence analysis is studied for the suggested basis expansion; some numerical results are exhibited to verify the applicability and accuracy of the method.
Related Topics
Concepts
Mathematics
Chebyshev polynomials
Fractional calculus
Convergence (economics)
Chebyshev filter
Basis function
Spectral method
Dimension (graph theory)
Applied mathematics
Boundary value problem
Basis (linear algebra)
Homogeneous
Orthogonal polynomials
Mathematical analysis
Boundary (topology)
Spectral element method
Algorithm
Chebyshev equation
Chebyshev pseudospectral method
Spectral analysis
Rate of convergence
Jacobi polynomials
Chebyshev iteration
Numerical analysis
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3846/mma.2025.22745
- https://journals.vilniustech.lt/index.php/MMA/article/download/22745/13071
- OA Status
- diamond
- References
- 31
- OpenAlex ID
- https://openalex.org/W7104600676
All OpenAlex metadata
Raw OpenAlex JSON
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https://openalex.org/W7104600676Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3846/mma.2025.22745Digital Object Identifier
- Title
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Spectral algorithm for fractional BVPs via novel modified Chebyshev polynomials fractional derivativesWork 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
-
2025-11-11Full publication date if available
- Authors
-
Mohamed Abdelhakem, Dina Abdelhamied, Mamdouh El-kady, Youssri Hassan YoussriList of authors in order
- Landing page
-
https://doi.org/10.3846/mma.2025.22745Publisher landing page
- PDF URL
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https://journals.vilniustech.lt/index.php/MMA/article/download/22745/13071Direct link to full text PDF
- Open access
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YesWhether a free full text is available
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diamondOpen access status per OpenAlex
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https://journals.vilniustech.lt/index.php/MMA/article/download/22745/13071Direct OA link when available
- Concepts
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Mathematics, Chebyshev polynomials, Fractional calculus, Convergence (economics), Chebyshev filter, Basis function, Spectral method, Dimension (graph theory), Applied mathematics, Boundary value problem, Basis (linear algebra), Homogeneous, Orthogonal polynomials, Mathematical analysis, Boundary (topology), Spectral element method, Algorithm, Chebyshev equation, Chebyshev pseudospectral method, Spectral analysis, Rate of convergence, Jacobi polynomials, Chebyshev iteration, Numerical analysisTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- References (count)
-
31Number of works referenced by this work
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| referenced_works | https://openalex.org/W4408995617, https://openalex.org/W4406605389, https://openalex.org/W4313907782, https://openalex.org/W4404657346, https://openalex.org/W3208208251, https://openalex.org/W4386073017, https://openalex.org/W4379511457, https://openalex.org/W3165843745, https://openalex.org/W4379511774, https://openalex.org/W3128184879, https://openalex.org/W3042974430, https://openalex.org/W4225426987, https://openalex.org/W4323847894, https://openalex.org/W4220899192, https://openalex.org/W3164875500, https://openalex.org/W4389580473, https://openalex.org/W4408286226, https://openalex.org/W4322623035, https://openalex.org/W4283080747, https://openalex.org/W4385648523, https://openalex.org/W4323275389, https://openalex.org/W4254246953, https://openalex.org/W3047917953, https://openalex.org/W4361275458, https://openalex.org/W4360991076, https://openalex.org/W4361275482, https://openalex.org/W4324195792, https://openalex.org/W4377137445, https://openalex.org/W3138864393, https://openalex.org/W4318819666, https://openalex.org/W4220842969 |
| referenced_works_count | 31 |
| abstract_inverted_index.a | 3 |
| abstract_inverted_index.in | 32 |
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| abstract_inverted_index.are | 57, 77 |
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| abstract_inverted_index.employs | 40 |
| abstract_inverted_index.method. | 87 |
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| abstract_inverted_index.suggested | 71 |
| abstract_inverted_index.expansion; | 73 |
| abstract_inverted_index.facilitate | 60 |
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| abstract_inverted_index.introduces | 2 |
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| abstract_inverted_index.conditions. | 53 |
| abstract_inverted_index.convergence | 65 |
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| abstract_inverted_index.homogeneous | 51 |
| abstract_inverted_index.polynomials | 47 |
| abstract_inverted_index.polynomials. | 21 |
| abstract_inverted_index.Specifically, | 22 |
| abstract_inverted_index.applicability | 82 |
| cited_by_percentile_year | |
| countries_distinct_count | 1 |
| institutions_distinct_count | 4 |
| citation_normalized_percentile.value | 0.77756242 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |