{"id":"https://openalex.org/W2053759540","doi":"https://doi.org/10.2478/v10006-011-0042-x","title":"An operational Haar wavelet method for solving fractional Volterra integral equations","display_name":"An operational Haar wavelet method for solving fractional Volterra integral equations","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W2053759540","doi":"https://doi.org/10.2478/v10006-011-0042-x","mag":"2053759540"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-011-0042-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0042-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0042-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-011-0042-x","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5060399386","display_name":"Habibollah Saeedi","orcid":"https://orcid.org/0000-0001-5627-9678"},"institutions":[{"id":"https://openalex.org/I115566878","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77","country_code":"IR","type":"education","lineage":["https://openalex.org/I115566878"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Habibollah Saeedi","raw_affiliation_strings":["Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran#TAB#","institution_ids":["https://openalex.org/I115566878"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010647696","display_name":"Nasibeh Mollahasani","orcid":"https://orcid.org/0000-0001-9291-1394"},"institutions":[{"id":"https://openalex.org/I115566878","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77","country_code":"IR","type":"education","lineage":["https://openalex.org/I115566878"]},{"id":"https://openalex.org/I4210088122","display_name":"Institute of Theoretical and Experimental Biophysics","ror":"https://ror.org/008ebms37","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210088122","https://openalex.org/I4210129690"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE","IR","RU"],"is_corresponding":false,"raw_author_name":"Nasibeh Mollahasani","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","Institute of Theoretical and Experimental Biophysics Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia","Max Planck Institute for Mathematics in the Sciences (MIS) Inselstrasse 22, Leipzig 04103, Germany","Mahani Mathematical Research Center Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","institution_ids":["https://openalex.org/I115566878"]},{"raw_affiliation_string":"Institute of Theoretical and Experimental Biophysics Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia","institution_ids":["https://openalex.org/I4210088122"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences (MIS) Inselstrasse 22, Leipzig 04103, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Mahani Mathematical Research Center Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","institution_ids":["https://openalex.org/I115566878"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047649217","display_name":"M. Mohseni Moghadam","orcid":null},"institutions":[{"id":"https://openalex.org/I115566878","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77","country_code":"IR","type":"education","lineage":["https://openalex.org/I115566878"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mahmoud Moghadam","raw_affiliation_strings":["Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran#TAB#","institution_ids":["https://openalex.org/I115566878"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064151637","display_name":"Gennady N. Chuev","orcid":"https://orcid.org/0000-0002-8608-3753"},"institutions":[{"id":"https://openalex.org/I115566878","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77","country_code":"IR","type":"education","lineage":["https://openalex.org/I115566878"]},{"id":"https://openalex.org/I4210088122","display_name":"Institute of Theoretical and Experimental Biophysics","ror":"https://ror.org/008ebms37","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210088122","https://openalex.org/I4210129690"]},{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]}],"countries":["DE","IR","RU"],"is_corresponding":false,"raw_author_name":"Gennady Chuev","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","Mahani Mathematical Research Center Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","Max Planck Institute for Mathematics in the Sciences (MIS) Inselstrasse 22, Leipzig 04103, Germany","Institute of Theoretical and Experimental Biophysics Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematics and Computer Science Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","institution_ids":["https://openalex.org/I115566878"]},{"raw_affiliation_string":"Mahani Mathematical Research Center Shahid Bahonar University of Kerman, Kerman, 76169-14111, Iran","institution_ids":["https://openalex.org/I115566878"]},{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences (MIS) Inselstrasse 22, Leipzig 04103, Germany","institution_ids":["https://openalex.org/I4210091327"]},{"raw_affiliation_string":"Institute of Theoretical and Experimental Biophysics Russian Academy of Sciences, Pushchino, Moscow Region 142290, Russia","institution_ids":["https://openalex.org/I4210088122"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":3.2888,"has_fulltext":true,"cited_by_count":51,"citation_normalized_percentile":{"value":0.90909091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"21","issue":"3","first_page":"535","last_page":"547"},"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":0.9979000091552734,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9973000288009644,"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":0.7641607522964478},{"id":"https://openalex.org/keywords/haar-wavelet","display_name":"Haar wavelet","score":0.7602062225341797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.715619683265686},{"id":"https://openalex.org/keywords/haar","display_name":"Haar","score":0.6544824838638306},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.6301858425140381},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6149293184280396},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.5766125321388245},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5226718783378601},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4428960382938385},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3919001519680023},{"id":"https://openalex.org/keywords/wavelet-transform","display_name":"Wavelet transform","score":0.3490756154060364},{"id":"https://openalex.org/keywords/discrete-wavelet-transform","display_name":"Discrete wavelet transform","score":0.3312112092971802},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.14815247058868408},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14788910746574402},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04914179444313049}],"concepts":[{"id":"https://openalex.org/C21965488","wikidata":"https://www.wikidata.org/wiki/Q2632613","display_name":"Volterra integral equation","level":3,"score":0.7641607522964478},{"id":"https://openalex.org/C2780423554","wikidata":"https://www.wikidata.org/wiki/Q766198","display_name":"Haar wavelet","level":5,"score":0.7602062225341797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.715619683265686},{"id":"https://openalex.org/C187029792","wikidata":"https://www.wikidata.org/wiki/Q2179112","display_name":"Haar","level":3,"score":0.6544824838638306},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.6301858425140381},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6149293184280396},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.5766125321388245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5226718783378601},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4428960382938385},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3919001519680023},{"id":"https://openalex.org/C196216189","wikidata":"https://www.wikidata.org/wiki/Q2867","display_name":"Wavelet transform","level":3,"score":0.3490756154060364},{"id":"https://openalex.org/C46286280","wikidata":"https://www.wikidata.org/wiki/Q2414958","display_name":"Discrete wavelet transform","level":4,"score":0.3312112092971802},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.14815247058868408},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14788910746574402},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04914179444313049},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2478/v10006-011-0042-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0042-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0042-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1001.6385","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1001.6385","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mis.mpg.de/preprints/2009/preprint2009_80.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.390.6985","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.6985","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://matwbn.icm.edu.pl/ksiazki/amc/amc21/amc21312.pdf","raw_type":"text"},{"id":"pmh:oai:edoc.mpg.de:587598","is_oa":false,"landing_page_url":"http://edoc.mpg.de/587598","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","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":"International Journal of Applied Mathematics and Computer Science, v.21, 535-547 (2011)","raw_type":"Article"},{"id":"pmh:oai:zbc.uz.zgora.pl:46938","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=46938","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=paper&paper=572","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-011-0042-x","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-011-0042-x","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-011-0042-x","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Partnerships for the goals","id":"https://metadata.un.org/sdg/17","score":0.41999998688697815}],"awards":[],"funders":[{"id":"https://openalex.org/F4320324640","display_name":"Shahid Bahonar University of Kerman","ror":"https://ror.org/04zn42r77"},{"id":"https://openalex.org/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https://ror.org/00ez2he07"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2053759540.pdf","grobid_xml":"https://content.openalex.org/works/W2053759540.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W198964195","https://openalex.org/W1528987510","https://openalex.org/W1544641223","https://openalex.org/W1550268283","https://openalex.org/W1553338987","https://openalex.org/W1965500773","https://openalex.org/W1967247388","https://openalex.org/W1971075293","https://openalex.org/W1973020618","https://openalex.org/W1973418968","https://openalex.org/W1978256444","https://openalex.org/W1980564965","https://openalex.org/W1985312627","https://openalex.org/W1986995623","https://openalex.org/W1993080951","https://openalex.org/W1993445800","https://openalex.org/W1998561306","https://openalex.org/W2006763907","https://openalex.org/W2013458971","https://openalex.org/W2020771042","https://openalex.org/W2025602190","https://openalex.org/W2041752335","https://openalex.org/W2052963592","https://openalex.org/W2067009585","https://openalex.org/W2072757689","https://openalex.org/W2080059419","https://openalex.org/W2087000533","https://openalex.org/W2087293778","https://openalex.org/W2101789093","https://openalex.org/W2107315434","https://openalex.org/W2116807840","https://openalex.org/W2123764525","https://openalex.org/W2153730510","https://openalex.org/W2314221121","https://openalex.org/W2787959293","https://openalex.org/W4229951323","https://openalex.org/W4247861852"],"related_works":["https://openalex.org/W1523827626","https://openalex.org/W2377605153","https://openalex.org/W634117680","https://openalex.org/W191391683","https://openalex.org/W1929885588","https://openalex.org/W2545237249","https://openalex.org/W2537072258","https://openalex.org/W5462945","https://openalex.org/W1533388234","https://openalex.org/W2115855844"],"abstract_inverted_index":{"An":[0],"operational":[1,14],"Haar":[2,12,28],"wavelet":[3,13,29],"method":[4,31],"for":[5],"solving":[6],"fractional":[7,19,37],"Volterra":[8,38],"integral":[9,41],"equations":[10,42],"A":[11,49],"matrix":[15],"is":[16,32,53],"applied":[17],"to":[18,34,43,67],"integration,":[20],"which":[21],"has":[22],"not":[23],"been":[24],"undertaken":[25],"before.":[26],"The":[27],"approximating":[30],"used":[33],"reduce":[35],"the":[36,69,74],"and":[39,55,62,71],"Abel":[40],"a":[44],"system":[45],"of":[46,73],"algebraic":[47],"equations.":[48],"global":[50],"error":[51],"bound":[52],"estimated":[54],"some":[56],"numerical":[57],"examples":[58],"with":[59],"smooth,":[60],"nonsmooth,":[61],"singular":[63],"solutions":[64],"are":[65],"considered":[66],"demonstrate":[68],"validity":[70],"applicability":[72],"developed":[75],"method.":[76]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":8},{"year":2012,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}