{"id":"https://openalex.org/W2996717176","doi":"https://doi.org/10.1155/2019/5678103","title":"Numerical Techniques for Solving Linear Volterra Fractional Integral Equation","display_name":"Numerical Techniques for Solving Linear Volterra Fractional Integral Equation","publication_year":2019,"publication_date":"2019-12-20","ids":{"openalex":"https://openalex.org/W2996717176","doi":"https://doi.org/10.1155/2019/5678103","mag":"2996717176"},"language":"en","primary_location":{"id":"doi:10.1155/2019/5678103","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5678103","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/5678103.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2019/5678103.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014344740","display_name":"S. M. Hamdan","orcid":null},"institutions":[{"id":"https://openalex.org/I17533244","display_name":"An-Najah National University","ror":"https://ror.org/0046mja08","country_code":"PS","type":"education","lineage":["https://openalex.org/I17533244"]}],"countries":["PS"],"is_corresponding":false,"raw_author_name":"Safa\u2019 Hamdan","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine","institution_ids":["https://openalex.org/I17533244"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083199759","display_name":"Naji Qatanani","orcid":"https://orcid.org/0000-0002-3008-495X"},"institutions":[{"id":"https://openalex.org/I17533244","display_name":"An-Najah National University","ror":"https://ror.org/0046mja08","country_code":"PS","type":"education","lineage":["https://openalex.org/I17533244"]}],"countries":["PS"],"is_corresponding":true,"raw_author_name":"Naji Qatanani","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine"],"raw_orcid":"https://orcid.org/0000-0002-3008-495X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine","institution_ids":["https://openalex.org/I17533244"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073773922","display_name":"Adnan Daraghmeh","orcid":"https://orcid.org/0000-0002-4531-8392"},"institutions":[{"id":"https://openalex.org/I17533244","display_name":"An-Najah National University","ror":"https://ror.org/0046mja08","country_code":"PS","type":"education","lineage":["https://openalex.org/I17533244"]}],"countries":["PS"],"is_corresponding":true,"raw_author_name":"Adnan Daraghmeh","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine"],"raw_orcid":"https://orcid.org/0000-0002-4531-8392","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, An-Najah National University, Nablus, State of Palestine","institution_ids":["https://openalex.org/I17533244"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5073773922","https://openalex.org/A5083199759"],"corresponding_institution_ids":["https://openalex.org/I17533244"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.454,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62657644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"2019","issue":null,"first_page":"1","last_page":"9"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/volterra-integral-equation","display_name":"Volterra integral equation","score":0.7112640738487244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6669754981994629},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.5808494687080383},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5706474781036377},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5675139427185059},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5399641394615173},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5343005061149597},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.5228734016418457},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4862583875656128},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4289109408855438},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.3482036888599396},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3085649013519287},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22475790977478027},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.16846701502799988},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.09147822856903076}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7112640738487244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6669754981994629},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.5808494687080383},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5706474781036377},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5675139427185059},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5399641394615173},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5343005061149597},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5228734016418457},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4862583875656128},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4289109408855438},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.3482036888599396},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3085649013519287},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22475790977478027},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.16846701502799988},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.09147822856903076},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2019/5678103","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5678103","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/5678103.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1590199221","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1590199221","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:5678103","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2019/5678103.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:f1f7ceabfba44de38042bfa7fe0e4120","is_oa":false,"landing_page_url":"https://doaj.org/article/f1f7ceabfba44de38042bfa7fe0e4120","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2019 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2019/5678103","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2019/5678103","pdf_url":"https://downloads.hindawi.com/journals/jam/2019/5678103.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2996717176.pdf","grobid_xml":"https://content.openalex.org/works/W2996717176.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1973020618","https://openalex.org/W1985312627","https://openalex.org/W1986372629","https://openalex.org/W2020988386","https://openalex.org/W2048681994","https://openalex.org/W2051383784","https://openalex.org/W2078862466","https://openalex.org/W2079905092","https://openalex.org/W2090187181","https://openalex.org/W2134837756","https://openalex.org/W2187264218","https://openalex.org/W2616998410","https://openalex.org/W2775044746","https://openalex.org/W4237768080"],"related_works":["https://openalex.org/W2268268129","https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2184249577","https://openalex.org/W4254660938","https://openalex.org/W4246784705","https://openalex.org/W4233243960","https://openalex.org/W1945408838","https://openalex.org/W1539637428","https://openalex.org/W2253351617"],"abstract_inverted_index":{"Two":[0],"numerical":[1,37],"techniques,":[2],"namely,":[3],"Haar":[4],"Wavelet":[5],"and":[6,33],"the":[7,20,26,31,36,53,64,74],"product":[8,75],"integration":[9,76],"methods,":[10],"have":[11],"been":[12],"employed":[13],"to":[14],"give":[15],"an":[16],"approximate":[17],"solution":[18,45],"of":[19,25,35,55],"fractional":[21],"Volterra":[22],"integral":[23],"equation":[24],"second":[27],"kind.":[28],"To":[29],"test":[30],"applicability":[32],"efficiency":[34],"method,":[38],"two":[39],"illustrative":[40],"examples":[41],"with":[42,63],"known":[43],"exact":[44,65],"are":[46,58],"presented.":[47],"Numerical":[48],"results":[49,81],"show":[50],"clearly":[51],"that":[52,73],"accuracy":[54],"these":[56,70],"methods":[57,71],"in":[59],"a":[60],"good":[61],"agreement":[62],"solution.":[66],"A":[67],"comparison":[68],"between":[69],"shows":[72],"method":[77],"provides":[78],"more":[79],"accurate":[80],"than":[82],"its":[83],"counterpart.":[84]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
