Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre Wavelets Article Swipe
Fukang Yin
,
Jianping Wu
,
Hongze Leng
·
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.12783/dtetr/amsm2017/14832
YOU?
·
· 2017
· Open Access
·
· DOI: https://doi.org/10.12783/dtetr/amsm2017/14832
In this paper, a new general procedure of the integration operational matrix of fractional-order Legendre wavelets is presented and then used to obtain the numerical solution of fractional differential equations. The fractional derivative in these problems is in the Caputo sense. By using the operational matrix of fractional integration, the original fractional differential equation is converted into a nonlinear system of algebraic equations which can be solved by Newton’s method. The numerical results are compared with exact solutions and existing numerical solutions found in the literature and demonstrate the validity and applicability of the proposed method.
Related Topics
Concepts
Legendre wavelet
Mathematics
Fractional calculus
Algebraic equation
Legendre polynomials
Mathematical analysis
Applied mathematics
Matrix (chemical analysis)
Numerical analysis
Wavelet
Differential equation
Nonlinear system
Numerical integration
Wavelet transform
Computer science
Physics
Discrete wavelet transform
Quantum mechanics
Materials science
Artificial intelligence
Composite material
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.12783/dtetr/amsm2017/14832
- http://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347
- OA Status
- diamond
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W2887745146
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
-
https://openalex.org/W2887745146Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.12783/dtetr/amsm2017/14832Digital Object Identifier
- Title
-
Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre WaveletsWork title
- Type
-
articleOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2017Year of publication
- Publication date
-
2017-10-17Full publication date if available
- Authors
-
Fukang Yin, Jianping Wu, Hongze LengList of authors in order
- Landing page
-
https://doi.org/10.12783/dtetr/amsm2017/14832Publisher landing page
- PDF URL
-
https://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
diamondOpen access status per OpenAlex
- OA URL
-
https://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347Direct OA link when available
- Concepts
-
Legendre wavelet, Mathematics, Fractional calculus, Algebraic equation, Legendre polynomials, Mathematical analysis, Applied mathematics, Matrix (chemical analysis), Numerical analysis, Wavelet, Differential equation, Nonlinear system, Numerical integration, Wavelet transform, Computer science, Physics, Discrete wavelet transform, Quantum mechanics, Materials science, Artificial intelligence, Composite materialTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
Full payload
| id | https://openalex.org/W2887745146 |
|---|---|
| doi | https://doi.org/10.12783/dtetr/amsm2017/14832 |
| ids.doi | https://doi.org/10.12783/dtetr/amsm2017/14832 |
| ids.mag | 2887745146 |
| ids.openalex | https://openalex.org/W2887745146 |
| fwci | 0.0 |
| type | article |
| title | Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre Wavelets |
| biblio.issue | amsm |
| biblio.volume | |
| biblio.last_page | |
| biblio.first_page | |
| topics[0].id | https://openalex.org/T10288 |
| topics[0].field.id | https://openalex.org/fields/26 |
| topics[0].field.display_name | Mathematics |
| topics[0].score | 0.9995999932289124 |
| topics[0].domain.id | https://openalex.org/domains/3 |
| topics[0].domain.display_name | Physical Sciences |
| topics[0].subfield.id | https://openalex.org/subfields/2611 |
| topics[0].subfield.display_name | Modeling and Simulation |
| topics[0].display_name | Fractional Differential Equations Solutions |
| topics[1].id | https://openalex.org/T10248 |
| topics[1].field.id | https://openalex.org/fields/31 |
| topics[1].field.display_name | Physics and Astronomy |
| topics[1].score | 0.9728999733924866 |
| topics[1].domain.id | https://openalex.org/domains/3 |
| topics[1].domain.display_name | Physical Sciences |
| topics[1].subfield.id | https://openalex.org/subfields/3109 |
| topics[1].subfield.display_name | Statistical and Nonlinear Physics |
| topics[1].display_name | Nonlinear Waves and Solitons |
| topics[2].id | https://openalex.org/T11081 |
| topics[2].field.id | https://openalex.org/fields/22 |
| topics[2].field.display_name | Engineering |
| topics[2].score | 0.9674000144004822 |
| topics[2].domain.id | https://openalex.org/domains/3 |
| topics[2].domain.display_name | Physical Sciences |
| topics[2].subfield.id | https://openalex.org/subfields/2207 |
| topics[2].subfield.display_name | Control and Systems Engineering |
| topics[2].display_name | Advanced Control Systems Design |
| is_xpac | False |
| apc_list | |
| apc_paid | |
| concepts[0].id | https://openalex.org/C123769847 |
| concepts[0].level | 5 |
| concepts[0].score | 0.8301947116851807 |
| concepts[0].wikidata | https://www.wikidata.org/wiki/Q6517888 |
| concepts[0].display_name | Legendre wavelet |
| concepts[1].id | https://openalex.org/C33923547 |
| concepts[1].level | 0 |
| concepts[1].score | 0.7519114017486572 |
| concepts[1].wikidata | https://www.wikidata.org/wiki/Q395 |
| concepts[1].display_name | Mathematics |
| concepts[2].id | https://openalex.org/C154249771 |
| concepts[2].level | 2 |
| concepts[2].score | 0.7043190598487854 |
| concepts[2].wikidata | https://www.wikidata.org/wiki/Q1339058 |
| concepts[2].display_name | Fractional calculus |
| concepts[3].id | https://openalex.org/C23917780 |
| concepts[3].level | 3 |
| concepts[3].score | 0.6523564457893372 |
| concepts[3].wikidata | https://www.wikidata.org/wiki/Q50698 |
| concepts[3].display_name | Algebraic equation |
| concepts[4].id | https://openalex.org/C111458787 |
| concepts[4].level | 2 |
| concepts[4].score | 0.5721564888954163 |
| concepts[4].wikidata | https://www.wikidata.org/wiki/Q215405 |
| concepts[4].display_name | Legendre polynomials |
| concepts[5].id | https://openalex.org/C134306372 |
| concepts[5].level | 1 |
| concepts[5].score | 0.5334278345108032 |
| concepts[5].wikidata | https://www.wikidata.org/wiki/Q7754 |
| concepts[5].display_name | Mathematical analysis |
| concepts[6].id | https://openalex.org/C28826006 |
| concepts[6].level | 1 |
| concepts[6].score | 0.4938879609107971 |
| concepts[6].wikidata | https://www.wikidata.org/wiki/Q33521 |
| concepts[6].display_name | Applied mathematics |
| concepts[7].id | https://openalex.org/C106487976 |
| concepts[7].level | 2 |
| concepts[7].score | 0.4870636761188507 |
| concepts[7].wikidata | https://www.wikidata.org/wiki/Q685816 |
| concepts[7].display_name | Matrix (chemical analysis) |
| concepts[8].id | https://openalex.org/C48753275 |
| concepts[8].level | 2 |
| concepts[8].score | 0.48543673753738403 |
| concepts[8].wikidata | https://www.wikidata.org/wiki/Q11216 |
| concepts[8].display_name | Numerical analysis |
| concepts[9].id | https://openalex.org/C47432892 |
| concepts[9].level | 2 |
| concepts[9].score | 0.47281304001808167 |
| concepts[9].wikidata | https://www.wikidata.org/wiki/Q831390 |
| concepts[9].display_name | Wavelet |
| concepts[10].id | https://openalex.org/C78045399 |
| concepts[10].level | 2 |
| concepts[10].score | 0.4346684515476227 |
| concepts[10].wikidata | https://www.wikidata.org/wiki/Q11214 |
| concepts[10].display_name | Differential equation |
| concepts[11].id | https://openalex.org/C158622935 |
| concepts[11].level | 2 |
| concepts[11].score | 0.42858487367630005 |
| concepts[11].wikidata | https://www.wikidata.org/wiki/Q660848 |
| concepts[11].display_name | Nonlinear system |
| concepts[12].id | https://openalex.org/C127349201 |
| concepts[12].level | 2 |
| concepts[12].score | 0.41601842641830444 |
| concepts[12].wikidata | https://www.wikidata.org/wiki/Q753445 |
| concepts[12].display_name | Numerical integration |
| concepts[13].id | https://openalex.org/C196216189 |
| concepts[13].level | 3 |
| concepts[13].score | 0.11446511745452881 |
| concepts[13].wikidata | https://www.wikidata.org/wiki/Q2867 |
| concepts[13].display_name | Wavelet transform |
| concepts[14].id | https://openalex.org/C41008148 |
| concepts[14].level | 0 |
| concepts[14].score | 0.11207601428031921 |
| concepts[14].wikidata | https://www.wikidata.org/wiki/Q21198 |
| concepts[14].display_name | Computer science |
| concepts[15].id | https://openalex.org/C121332964 |
| concepts[15].level | 0 |
| concepts[15].score | 0.06658220291137695 |
| concepts[15].wikidata | https://www.wikidata.org/wiki/Q413 |
| concepts[15].display_name | Physics |
| concepts[16].id | https://openalex.org/C46286280 |
| concepts[16].level | 4 |
| concepts[16].score | 0.05835077166557312 |
| concepts[16].wikidata | https://www.wikidata.org/wiki/Q2414958 |
| concepts[16].display_name | Discrete wavelet transform |
| concepts[17].id | https://openalex.org/C62520636 |
| concepts[17].level | 1 |
| concepts[17].score | 0.0 |
| concepts[17].wikidata | https://www.wikidata.org/wiki/Q944 |
| concepts[17].display_name | Quantum mechanics |
| concepts[18].id | https://openalex.org/C192562407 |
| concepts[18].level | 0 |
| concepts[18].score | 0.0 |
| concepts[18].wikidata | https://www.wikidata.org/wiki/Q228736 |
| concepts[18].display_name | Materials science |
| concepts[19].id | https://openalex.org/C154945302 |
| concepts[19].level | 1 |
| concepts[19].score | 0.0 |
| concepts[19].wikidata | https://www.wikidata.org/wiki/Q11660 |
| concepts[19].display_name | Artificial intelligence |
| concepts[20].id | https://openalex.org/C159985019 |
| concepts[20].level | 1 |
| concepts[20].score | 0.0 |
| concepts[20].wikidata | https://www.wikidata.org/wiki/Q181790 |
| concepts[20].display_name | Composite material |
| keywords[0].id | https://openalex.org/keywords/legendre-wavelet |
| keywords[0].score | 0.8301947116851807 |
| keywords[0].display_name | Legendre wavelet |
| keywords[1].id | https://openalex.org/keywords/mathematics |
| keywords[1].score | 0.7519114017486572 |
| keywords[1].display_name | Mathematics |
| keywords[2].id | https://openalex.org/keywords/fractional-calculus |
| keywords[2].score | 0.7043190598487854 |
| keywords[2].display_name | Fractional calculus |
| keywords[3].id | https://openalex.org/keywords/algebraic-equation |
| keywords[3].score | 0.6523564457893372 |
| keywords[3].display_name | Algebraic equation |
| keywords[4].id | https://openalex.org/keywords/legendre-polynomials |
| keywords[4].score | 0.5721564888954163 |
| keywords[4].display_name | Legendre polynomials |
| keywords[5].id | https://openalex.org/keywords/mathematical-analysis |
| keywords[5].score | 0.5334278345108032 |
| keywords[5].display_name | Mathematical analysis |
| keywords[6].id | https://openalex.org/keywords/applied-mathematics |
| keywords[6].score | 0.4938879609107971 |
| keywords[6].display_name | Applied mathematics |
| keywords[7].id | https://openalex.org/keywords/matrix |
| keywords[7].score | 0.4870636761188507 |
| keywords[7].display_name | Matrix (chemical analysis) |
| keywords[8].id | https://openalex.org/keywords/numerical-analysis |
| keywords[8].score | 0.48543673753738403 |
| keywords[8].display_name | Numerical analysis |
| keywords[9].id | https://openalex.org/keywords/wavelet |
| keywords[9].score | 0.47281304001808167 |
| keywords[9].display_name | Wavelet |
| keywords[10].id | https://openalex.org/keywords/differential-equation |
| keywords[10].score | 0.4346684515476227 |
| keywords[10].display_name | Differential equation |
| keywords[11].id | https://openalex.org/keywords/nonlinear-system |
| keywords[11].score | 0.42858487367630005 |
| keywords[11].display_name | Nonlinear system |
| keywords[12].id | https://openalex.org/keywords/numerical-integration |
| keywords[12].score | 0.41601842641830444 |
| keywords[12].display_name | Numerical integration |
| keywords[13].id | https://openalex.org/keywords/wavelet-transform |
| keywords[13].score | 0.11446511745452881 |
| keywords[13].display_name | Wavelet transform |
| keywords[14].id | https://openalex.org/keywords/computer-science |
| keywords[14].score | 0.11207601428031921 |
| keywords[14].display_name | Computer science |
| keywords[15].id | https://openalex.org/keywords/physics |
| keywords[15].score | 0.06658220291137695 |
| keywords[15].display_name | Physics |
| keywords[16].id | https://openalex.org/keywords/discrete-wavelet-transform |
| keywords[16].score | 0.05835077166557312 |
| keywords[16].display_name | Discrete wavelet transform |
| language | en |
| locations[0].id | doi:10.12783/dtetr/amsm2017/14832 |
| locations[0].is_oa | True |
| locations[0].source.id | https://openalex.org/S2764531519 |
| locations[0].source.issn | 2475-885X |
| locations[0].source.type | journal |
| locations[0].source.is_oa | True |
| locations[0].source.issn_l | 2475-885X |
| locations[0].source.is_core | True |
| locations[0].source.is_in_doaj | False |
| locations[0].source.display_name | DEStech Transactions on Engineering and Technology Research |
| locations[0].source.host_organization | https://openalex.org/P4322697008 |
| locations[0].source.host_organization_name | Destech Publications |
| locations[0].source.host_organization_lineage | https://openalex.org/P4322697008 |
| locations[0].source.host_organization_lineage_names | Destech Publications |
| locations[0].license | |
| locations[0].pdf_url | http://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347 |
| locations[0].version | publishedVersion |
| locations[0].raw_type | journal-article |
| locations[0].license_id | |
| locations[0].is_accepted | True |
| locations[0].is_published | True |
| locations[0].raw_source_name | DEStech Transactions on Engineering and Technology Research |
| locations[0].landing_page_url | https://doi.org/10.12783/dtetr/amsm2017/14832 |
| indexed_in | crossref |
| authorships[0].author.id | https://openalex.org/A5089866247 |
| authorships[0].author.orcid | https://orcid.org/0000-0002-8353-7000 |
| authorships[0].author.display_name | Fukang Yin |
| authorships[0].author_position | first |
| authorships[0].raw_author_name | Fu-kang YIN |
| authorships[0].is_corresponding | False |
| authorships[1].author.id | https://openalex.org/A5001949272 |
| authorships[1].author.orcid | https://orcid.org/0000-0002-8887-8031 |
| authorships[1].author.display_name | Jianping Wu |
| authorships[1].author_position | middle |
| authorships[1].raw_author_name | Jian-ping WU |
| authorships[1].is_corresponding | False |
| authorships[2].author.id | https://openalex.org/A5087009225 |
| authorships[2].author.orcid | https://orcid.org/0000-0003-3338-7566 |
| authorships[2].author.display_name | Hongze Leng |
| authorships[2].author_position | last |
| authorships[2].raw_author_name | Hong-ze LENG |
| authorships[2].is_corresponding | False |
| has_content.pdf | True |
| has_content.grobid_xml | True |
| is_paratext | False |
| open_access.is_oa | True |
| open_access.oa_url | http://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347 |
| open_access.oa_status | diamond |
| open_access.any_repository_has_fulltext | False |
| created_date | 2025-10-10T00:00:00 |
| display_name | Numerical Solution of Fractional Differential Equations by Using Integration Operational Matrix of Fractional-Order Legendre Wavelets |
| has_fulltext | False |
| is_retracted | False |
| updated_date | 2025-11-06T03:46:38.306776 |
| primary_topic.id | https://openalex.org/T10288 |
| primary_topic.field.id | https://openalex.org/fields/26 |
| primary_topic.field.display_name | Mathematics |
| primary_topic.score | 0.9995999932289124 |
| primary_topic.domain.id | https://openalex.org/domains/3 |
| primary_topic.domain.display_name | Physical Sciences |
| primary_topic.subfield.id | https://openalex.org/subfields/2611 |
| primary_topic.subfield.display_name | Modeling and Simulation |
| primary_topic.display_name | Fractional Differential Equations Solutions |
| related_works | https://openalex.org/W2545227774, https://openalex.org/W3130851271, https://openalex.org/W2788092364, https://openalex.org/W4313180762, https://openalex.org/W2462438656, https://openalex.org/W2357310454, https://openalex.org/W2288349649, https://openalex.org/W2789913125, https://openalex.org/W2089945891, https://openalex.org/W2042250814 |
| cited_by_count | 0 |
| locations_count | 1 |
| best_oa_location.id | doi:10.12783/dtetr/amsm2017/14832 |
| best_oa_location.is_oa | True |
| best_oa_location.source.id | https://openalex.org/S2764531519 |
| best_oa_location.source.issn | 2475-885X |
| best_oa_location.source.type | journal |
| best_oa_location.source.is_oa | True |
| best_oa_location.source.issn_l | 2475-885X |
| best_oa_location.source.is_core | True |
| best_oa_location.source.is_in_doaj | False |
| best_oa_location.source.display_name | DEStech Transactions on Engineering and Technology Research |
| best_oa_location.source.host_organization | https://openalex.org/P4322697008 |
| best_oa_location.source.host_organization_name | Destech Publications |
| best_oa_location.source.host_organization_lineage | https://openalex.org/P4322697008 |
| best_oa_location.source.host_organization_lineage_names | Destech Publications |
| best_oa_location.license | |
| best_oa_location.pdf_url | http://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347 |
| best_oa_location.version | publishedVersion |
| best_oa_location.raw_type | journal-article |
| best_oa_location.license_id | |
| best_oa_location.is_accepted | True |
| best_oa_location.is_published | True |
| best_oa_location.raw_source_name | DEStech Transactions on Engineering and Technology Research |
| best_oa_location.landing_page_url | https://doi.org/10.12783/dtetr/amsm2017/14832 |
| primary_location.id | doi:10.12783/dtetr/amsm2017/14832 |
| primary_location.is_oa | True |
| primary_location.source.id | https://openalex.org/S2764531519 |
| primary_location.source.issn | 2475-885X |
| primary_location.source.type | journal |
| primary_location.source.is_oa | True |
| primary_location.source.issn_l | 2475-885X |
| primary_location.source.is_core | True |
| primary_location.source.is_in_doaj | False |
| primary_location.source.display_name | DEStech Transactions on Engineering and Technology Research |
| primary_location.source.host_organization | https://openalex.org/P4322697008 |
| primary_location.source.host_organization_name | Destech Publications |
| primary_location.source.host_organization_lineage | https://openalex.org/P4322697008 |
| primary_location.source.host_organization_lineage_names | Destech Publications |
| primary_location.license | |
| primary_location.pdf_url | http://dpi-proceedings.com/index.php/dtetr/article/download/14832/14347 |
| primary_location.version | publishedVersion |
| primary_location.raw_type | journal-article |
| primary_location.license_id | |
| primary_location.is_accepted | True |
| primary_location.is_published | True |
| primary_location.raw_source_name | DEStech Transactions on Engineering and Technology Research |
| primary_location.landing_page_url | https://doi.org/10.12783/dtetr/amsm2017/14832 |
| publication_date | 2017-10-17 |
| publication_year | 2017 |
| referenced_works_count | 0 |
| abstract_inverted_index.a | 3, 57 |
| abstract_inverted_index.By | 41 |
| abstract_inverted_index.In | 0 |
| abstract_inverted_index.be | 65 |
| abstract_inverted_index.by | 67 |
| abstract_inverted_index.in | 33, 37, 83 |
| abstract_inverted_index.is | 16, 36, 54 |
| abstract_inverted_index.of | 7, 12, 26, 46, 60, 92 |
| abstract_inverted_index.to | 21 |
| abstract_inverted_index.The | 30, 70 |
| abstract_inverted_index.and | 18, 78, 86, 90 |
| abstract_inverted_index.are | 73 |
| abstract_inverted_index.can | 64 |
| abstract_inverted_index.new | 4 |
| abstract_inverted_index.the | 8, 23, 38, 43, 49, 84, 88, 93 |
| abstract_inverted_index.into | 56 |
| abstract_inverted_index.then | 19 |
| abstract_inverted_index.this | 1 |
| abstract_inverted_index.used | 20 |
| abstract_inverted_index.with | 75 |
| abstract_inverted_index.exact | 76 |
| abstract_inverted_index.found | 82 |
| abstract_inverted_index.these | 34 |
| abstract_inverted_index.using | 42 |
| abstract_inverted_index.which | 63 |
| abstract_inverted_index.Caputo | 39 |
| abstract_inverted_index.matrix | 11, 45 |
| abstract_inverted_index.obtain | 22 |
| abstract_inverted_index.paper, | 2 |
| abstract_inverted_index.sense. | 40 |
| abstract_inverted_index.solved | 66 |
| abstract_inverted_index.system | 59 |
| abstract_inverted_index.general | 5 |
| abstract_inverted_index.method. | 69, 95 |
| abstract_inverted_index.results | 72 |
| abstract_inverted_index.Legendre | 14 |
| abstract_inverted_index.compared | 74 |
| abstract_inverted_index.equation | 53 |
| abstract_inverted_index.existing | 79 |
| abstract_inverted_index.original | 50 |
| abstract_inverted_index.problems | 35 |
| abstract_inverted_index.proposed | 94 |
| abstract_inverted_index.solution | 25 |
| abstract_inverted_index.validity | 89 |
| abstract_inverted_index.wavelets | 15 |
| abstract_inverted_index.algebraic | 61 |
| abstract_inverted_index.converted | 55 |
| abstract_inverted_index.equations | 62 |
| abstract_inverted_index.nonlinear | 58 |
| abstract_inverted_index.numerical | 24, 71, 80 |
| abstract_inverted_index.presented | 17 |
| abstract_inverted_index.procedure | 6 |
| abstract_inverted_index.solutions | 77, 81 |
| abstract_inverted_index.derivative | 32 |
| abstract_inverted_index.equations. | 29 |
| abstract_inverted_index.fractional | 27, 31, 47, 51 |
| abstract_inverted_index.literature | 85 |
| abstract_inverted_index.demonstrate | 87 |
| abstract_inverted_index.integration | 9 |
| abstract_inverted_index.operational | 10, 44 |
| abstract_inverted_index.differential | 28, 52 |
| abstract_inverted_index.integration, | 48 |
| abstract_inverted_index.applicability | 91 |
| abstract_inverted_index.Newton’s | 68 |
| abstract_inverted_index.fractional-order | 13 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| citation_normalized_percentile.value | 0.18416887 |
| citation_normalized_percentile.is_in_top_1_percent | False |
| citation_normalized_percentile.is_in_top_10_percent | False |