{"id":"https://openalex.org/W3203166407","doi":"https://doi.org/10.13189/ms.2021.090519","title":"The Fractional Residual Power Series Method for Solving a System of Linear Fractional Fredholm Integro-differential Equations","display_name":"The Fractional Residual Power Series Method for Solving a System of Linear Fractional Fredholm Integro-differential Equations","publication_year":2021,"publication_date":"2021-09-01","ids":{"openalex":"https://openalex.org/W3203166407","doi":"https://doi.org/10.13189/ms.2021.090519","mag":"3203166407"},"language":"en","primary_location":{"id":"doi:10.13189/ms.2021.090519","doi":"https://doi.org/10.13189/ms.2021.090519","is_oa":true,"landing_page_url":"https://doi.org/10.13189/ms.2021.090519","pdf_url":"http://www.hrpub.org/download/20210930/MS19-13424533.pdf","source":{"id":"https://openalex.org/S2764493858","display_name":"Mathematics and Statistics","issn_l":"2332-2071","issn":["2332-2071","2332-2144"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4324001558","host_organization_name":"Horizon Research Publishing","host_organization_lineage":["https://openalex.org/P4324001558"],"host_organization_lineage_names":["Horizon Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Statistics","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W3203166407"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://www.hrpub.org/download/20210930/MS19-13424533.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078659332","display_name":"Prapart Pue-on","orcid":"https://orcid.org/0000-0001-9311-8371","observed_orcids":["https://orcid.org/0000-0001-9311-8371"]},"institutions":[{"id":"https://openalex.org/I123096312","display_name":"Mahasarakham University","ror":"https://ror.org/0453j3c58","country_code":"TH","type":"education","lineage":["https://openalex.org/I123096312"]}],"countries":["TH"],"is_corresponding":true,"raw_author_name":"Prapart Pue-on","raw_affiliation_strings":["Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand","institution_ids":["https://openalex.org/I123096312"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5078659332"],"corresponding_institution_ids":["https://openalex.org/I123096312"],"apc_list":null,"apc_paid":null,"fwci":0.1776,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.44990882,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"9","issue":"5","first_page":"792","last_page":"798"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9951000213623047,"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":0.9951000213623047,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.0020000000949949026,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.0010000000474974513,"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/systems-of-integro-differential-equations","display_name":"systems of integro-differential equations","score":0.9399999976158142},{"id":"https://openalex.org/keywords/caputo-fractional-derivative","display_name":"Caputo fractional derivative","score":0.9940000176429749},{"id":"https://openalex.org/keywords/residual-function","display_name":"residual function","score":0.8550000190734863},{"id":"https://openalex.org/keywords/numerical-solution-of-fractional-equations","display_name":"numerical solution of fractional equations","score":0.5989999771118164}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9059524536132812},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.6846092343330383},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.584945559501648},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5650092959403992},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.541377604007721},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5082506537437439},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.48321282863616943},{"id":"https://openalex.org/C159674985","wikidata":"https://www.wikidata.org/wiki/Q6823718","display_name":"Method of mean weighted residuals","level":4,"score":0.46229785680770874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4546220600605011},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.32781916856765747},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2941906452178955},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0784071683883667},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.13189/ms.2021.090519","doi":"https://doi.org/10.13189/ms.2021.090519","is_oa":true,"landing_page_url":"https://doi.org/10.13189/ms.2021.090519","pdf_url":"http://www.hrpub.org/download/20210930/MS19-13424533.pdf","source":{"id":"https://openalex.org/S2764493858","display_name":"Mathematics and Statistics","issn_l":"2332-2071","issn":["2332-2071","2332-2144"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4324001558","host_organization_name":"Horizon Research Publishing","host_organization_lineage":["https://openalex.org/P4324001558"],"host_organization_lineage_names":["Horizon Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Statistics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.13189/ms.2021.090519","doi":"https://doi.org/10.13189/ms.2021.090519","is_oa":true,"landing_page_url":"https://doi.org/10.13189/ms.2021.090519","pdf_url":"http://www.hrpub.org/download/20210930/MS19-13424533.pdf","source":{"id":"https://openalex.org/S2764493858","display_name":"Mathematics and Statistics","issn_l":"2332-2071","issn":["2332-2071","2332-2144"],"is_oa":true,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4324001558","host_organization_name":"Horizon Research Publishing","host_organization_lineage":["https://openalex.org/P4324001558"],"host_organization_lineage_names":["Horizon Research Publishing"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics and Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324290","display_name":"Mahasarakham University","ror":"https://ror.org/0453j3c58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3203166407.pdf","grobid_xml":"https://content.openalex.org/works/W3203166407.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1541906269","https://openalex.org/W1584611818","https://openalex.org/W1600500744","https://openalex.org/W2006205876","https://openalex.org/W2041509648","https://openalex.org/W2041875300","https://openalex.org/W2052105007","https://openalex.org/W2301349605","https://openalex.org/W2321307647","https://openalex.org/W2344316029","https://openalex.org/W2346958621","https://openalex.org/W2380392230","https://openalex.org/W2586992596","https://openalex.org/W2602512207","https://openalex.org/W2745199247","https://openalex.org/W2758683176","https://openalex.org/W2811043253","https://openalex.org/W2888648338","https://openalex.org/W2896541796","https://openalex.org/W2932001993","https://openalex.org/W2937097319","https://openalex.org/W3024559098","https://openalex.org/W3185442798","https://openalex.org/W4243682544"],"related_works":["https://openalex.org/W2745199247","https://openalex.org/W2944627102","https://openalex.org/W3166517873","https://openalex.org/W2956152145","https://openalex.org/W3048930411","https://openalex.org/W3207523468","https://openalex.org/W3106896274","https://openalex.org/W4378469080","https://openalex.org/W2954090117","https://openalex.org/W4407309239"],"abstract_inverted_index":{"In":[0],"this":[1,26],"manuscript,":[2],"the":[3,33,49,57,65,68,85,96,103,113,118,122,125,136,142,153,163,181,198,204,209,214],"fractional":[4,18,43,69,126,144],"residual":[5,81,104],"power":[6,91,114,127,145],"series":[7,60,92,115,128,146],"(FRPS)":[8],"method":[9,54,177],"is":[10,46,73,172],"employed":[11],"in":[12,28,48],"solving":[13],"a":[14,38,80,109,140,189],"system":[15,27,111,120],"of":[16,25,35,42,71,88,124,139,155,180,213],"linear":[17,110,119],"Fredholm":[19],"integro-differential":[20],"equations.":[21],"The":[22,40,52,75],"significant":[23],"role":[24],"various":[29],"fields":[30],"has":[31,152],"attracted":[32],"attention":[34],"researchers":[36],"for":[37,112,178],"decade.":[39],"definition":[41],"derivative":[44,70],"here":[45],"described":[47],"Caputo":[50],"sense.":[51],"proposed":[53],"relies":[55],"on":[56,169],"generalized":[58],"Taylor":[59],"expansion":[61],"as":[62,64],"well":[63],"fact":[66],"that":[67,94],"stationary":[72],"zero.":[74],"process":[76],"starts":[77],"by":[78,83,131],"constructing":[79],"function":[82],"supposing":[84],"finite":[86],"order":[87],"an":[89,175],"approximate":[90,143],"solution":[93,207],"prescribes":[95],"initial":[97],"conditions.":[98],"Then,":[99],"utilizing":[100],"some":[101],"conditions,":[102],"functions":[105],"are":[106,148],"converted":[107],"to":[108,158,162],"coefficients.":[116],"Solving":[117],"reveals":[121],"coefficients":[123,134],"solution.":[129],"Finally,":[130],"substituting":[132],"these":[133],"into":[135],"supposed":[137],"form":[138],"solution,":[141],"solutions":[147,196],"derived.":[149],"This":[150],"technique":[151],"advantage":[154],"being":[156],"able":[157],"be":[159],"applied":[160],"directly":[161],"problem":[164],"and":[165,201,211],"spending":[166],"less":[167],"time":[168],"computation.":[170],"It":[171],"not":[173],"only":[174],"easy":[176],"implementation":[179],"problem,":[182],"but":[183],"also":[184],"provides":[185],"productive":[186],"results":[187],"after":[188],"few":[190],"iterations.":[191],"Some":[192],"problems":[193],"with":[194],"known":[195],"emphasize":[197],"procedure's":[199],"simplicity":[200],"reliability.":[202],"Moreover,":[203],"obtained":[205],"exact":[206],"demonstrated":[208],"efficiency":[210],"accuracy":[212],"presented":[215],"method.":[216]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2021-10-11T00:00:00"}
