Solution of fractional boundary value problems by $ \psi $-shifted operational matrices Article Swipe
Shazia Sadiq
,
Mujeeb ur Rehman
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3934/math.2022372
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.3934/math.2022372
In this paper, a numerical method is presented to solve fractional boundary value problems. In fractional calculus, the modelling of natural phenomenons is best described by fractional differential equations. So, it is important to formulate efficient and accurate numerical techniques to solve fractional differential equations. In this article, first, we introduce $ \psi $-shifted Chebyshev polynomials then project these polynomials to formulate $ \psi $-shifted Chebyshev operational matrices. Finally, these operational matrices are used for the solution of fractional boundary value problems. The convergence is analysed. It is observed that solution of non-integer order differential equation converges to corresponding solution of integer order differential equation. Finally, the efficiency and applicability of method is tested by comparison of the method with some other existing methods.
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- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.3934/math.2022372
- OA Status
- gold
- Cited By
- 12
- References
- 40
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4206986505
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4206986505Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.3934/math.2022372Digital Object Identifier
- Title
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Solution of fractional boundary value problems by $ \psi $-shifted operational matricesWork title
- Type
-
articleOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-01-01Full publication date if available
- Authors
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Shazia Sadiq, Mujeeb ur RehmanList of authors in order
- Landing page
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https://doi.org/10.3934/math.2022372Publisher landing page
- Open access
-
YesWhether a free full text is available
- OA status
-
goldOpen access status per OpenAlex
- OA URL
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https://doi.org/10.3934/math.2022372Direct OA link when available
- Concepts
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Mathematics, Boundary value problem, Integer (computer science), Fractional calculus, Chebyshev polynomials, Convergence (economics), Chebyshev filter, Order (exchange), Differential equation, Applied mathematics, Mathematical analysis, Computer science, Finance, Programming language, Economics, Economic growthTop concepts (fields/topics) attached by OpenAlex
- Cited by
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12Total citation count in OpenAlex
- Citations by year (recent)
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2025: 2, 2024: 7, 2023: 3Per-year citation counts (last 5 years)
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40Number of works referenced by this work
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.formulate | 34, 61 |
| abstract_inverted_index.important | 32 |
| abstract_inverted_index.introduce | 50 |
| abstract_inverted_index.matrices. | 67 |
| abstract_inverted_index.modelling | 18 |
| abstract_inverted_index.numerical | 4, 38 |
| abstract_inverted_index.presented | 7 |
| abstract_inverted_index.problems. | 13, 81 |
| abstract_inverted_index.comparison | 115 |
| abstract_inverted_index.efficiency | 107 |
| abstract_inverted_index.equations. | 28, 44 |
| abstract_inverted_index.fractional | 10, 15, 26, 42, 78 |
| abstract_inverted_index.techniques | 39 |
| abstract_inverted_index.convergence | 83 |
| abstract_inverted_index.non-integer | 92 |
| abstract_inverted_index.operational | 66, 70 |
| abstract_inverted_index.phenomenons | 21 |
| abstract_inverted_index.polynomials | 55, 59 |
| abstract_inverted_index.differential | 27, 43, 94, 103 |
| abstract_inverted_index.applicability | 109 |
| abstract_inverted_index.corresponding | 98 |
| abstract_inverted_index.<abstract><p>In | 0 |
| abstract_inverted_index.methods.</p></abstract> | 123 |
| cited_by_percentile_year.max | 99 |
| cited_by_percentile_year.min | 95 |
| corresponding_author_ids | https://openalex.org/A5008617568 |
| countries_distinct_count | 1 |
| institutions_distinct_count | 2 |
| corresponding_institution_ids | https://openalex.org/I929597975 |
| citation_normalized_percentile.value | 0.82797567 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |