{"id":"https://openalex.org/W3041661128","doi":"https://doi.org/10.1155/2020/7232907","title":"Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations","display_name":"Homotopy Analysis Method for Three Types of Fractional Partial Differential Equations","publication_year":2020,"publication_date":"2020-07-10","ids":{"openalex":"https://openalex.org/W3041661128","doi":"https://doi.org/10.1155/2020/7232907","mag":"3041661128"},"language":"en","primary_location":{"id":"doi:10.1155/2020/7232907","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/7232907","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/7232907.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","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/complexity/2020/7232907.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007206469","display_name":"Haidong Qu","orcid":"https://orcid.org/0000-0003-3528-4325"},"institutions":[{"id":"https://openalex.org/I4210165736","display_name":"Hanshan Normal University","ror":"https://ror.org/05tqaz865","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165736"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haidong Qu","raw_affiliation_strings":["Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China","institution_ids":["https://openalex.org/I4210165736"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072377026","display_name":"Zi\u2010Hang She","orcid":"https://orcid.org/0000-0001-9274-037X"},"institutions":[{"id":"https://openalex.org/I32574673","display_name":"Shantou University","ror":"https://ror.org/01a099706","country_code":"CN","type":"education","lineage":["https://openalex.org/I32574673"]},{"id":"https://openalex.org/I4210165736","display_name":"Hanshan Normal University","ror":"https://ror.org/05tqaz865","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165736"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zihang She","raw_affiliation_strings":["Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China","Department of Mathematics, Shantou University, Shantou 515063, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China","institution_ids":["https://openalex.org/I4210165736"]},{"raw_affiliation_string":"Department of Mathematics, Shantou University, Shantou 515063, China","institution_ids":["https://openalex.org/I32574673"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035005825","display_name":"Xuan Liu","orcid":"https://orcid.org/0000-0001-8028-2682"},"institutions":[{"id":"https://openalex.org/I4210165736","display_name":"Hanshan Normal University","ror":"https://ror.org/05tqaz865","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210165736"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xuan Liu","raw_affiliation_strings":["Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hanshan Normal University, Chaozhou 515041, China","institution_ids":["https://openalex.org/I4210165736"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5035005825"],"corresponding_institution_ids":["https://openalex.org/I4210165736"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.5252,"has_fulltext":true,"cited_by_count":22,"citation_normalized_percentile":{"value":0.73312214,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"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":0.9865000247955322,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9807000160217285,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8023346662521362},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7689471244812012},{"id":"https://openalex.org/keywords/homotopy-analysis-method","display_name":"Homotopy analysis method","score":0.5906742811203003},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5873672366142273},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5548725724220276},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.45882558822631836},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44059666991233826},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4170551300048828},{"id":"https://openalex.org/keywords/homotopy","display_name":"Homotopy","score":0.37394148111343384},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35962173342704773},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12694686651229858}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8023346662521362},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7689471244812012},{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.5906742811203003},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5873672366142273},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5548725724220276},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.45882558822631836},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44059666991233826},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4170551300048828},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.37394148111343384},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35962173342704773},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12694686651229858}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2020/7232907","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/7232907","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/7232907.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:7232907","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/7232907.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:afdec24dcea044268c37bd71f9bf88d9","is_oa":true,"landing_page_url":"https://doaj.org/article/afdec24dcea044268c37bd71f9bf88d9","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/7232907","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/7232907","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/7232907.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"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":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1231421488","display_name":null,"funder_award_id":"under","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G18853069","display_name":null,"funder_award_id":"2020KZDZX1147","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3803426314","display_name":null,"funder_award_id":"2017KQNCX130","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4020255992","display_name":null,"funder_award_id":"Project","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4068188220","display_name":null,"funder_award_id":"2017KQNCX130","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G411240615","display_name":null,"funder_award_id":"2018KQNCX156","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4548864725","display_name":null,"funder_award_id":"11771265","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"},{"id":"https://openalex.org/G5097798232","display_name":null,"funder_award_id":"11771265","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5939423041","display_name":null,"funder_award_id":"Technology","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6155239669","display_name":null,"funder_award_id":"2019GY02","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"},{"id":"https://openalex.org/G6218790471","display_name":null,"funder_award_id":"2018KQNCX156","funder_id":"https://openalex.org/F4320326279","funder_display_name":"Department of Education of Guangdong Province"},{"id":"https://openalex.org/G6581485291","display_name":null,"funder_award_id":"2020KZDZX1147","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G927583516","display_name":null,"funder_award_id":"2019GY02","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320326279","display_name":"Department of Education of Guangdong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3041661128.pdf","grobid_xml":"https://content.openalex.org/works/W3041661128.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1963563982","https://openalex.org/W1964964729","https://openalex.org/W1965027360","https://openalex.org/W1966793822","https://openalex.org/W1990709609","https://openalex.org/W1999302051","https://openalex.org/W1999340559","https://openalex.org/W2010031906","https://openalex.org/W2011242297","https://openalex.org/W2014666630","https://openalex.org/W2019469368","https://openalex.org/W2027205768","https://openalex.org/W2065261142","https://openalex.org/W2078643611","https://openalex.org/W2087034446","https://openalex.org/W2107162131","https://openalex.org/W2130620182","https://openalex.org/W2144522870","https://openalex.org/W2151901634","https://openalex.org/W2158267260","https://openalex.org/W2473914403","https://openalex.org/W2884885555","https://openalex.org/W2900472542","https://openalex.org/W2969085022","https://openalex.org/W2990918991"],"related_works":["https://openalex.org/W2362256999","https://openalex.org/W2470744056","https://openalex.org/W2007245702","https://openalex.org/W2359206539","https://openalex.org/W2048873866","https://openalex.org/W2388355944","https://openalex.org/W2479314534","https://openalex.org/W2025658988","https://openalex.org/W2563073486","https://openalex.org/W1991459776"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"three":[3],"types":[4],"of":[5,60,99,107,122],"fractional":[6,13,16,55,81,129],"order":[7,82,130],"partial":[8,23,131],"differential":[9,24,58,132],"equations,":[10],"including":[11],"the":[12,36,54,67,73,77,96,100,103,114,120,123],"Cauchy\u2013Riemann":[14],"equation,":[15,19],"acoustic":[17],"wave":[18],"and":[20,30,57,110],"two-dimensional":[21],"space":[22],"equation":[25],"with":[26,44,86],"time-fractional-order,":[27],"are":[28,33,64,91],"considered,":[29],"these":[31],"models":[32,83],"obtained":[34],"from":[35,66],"standard":[37],"equations":[38],"by":[39,71],"replacing":[40],"an":[41],"integer-order":[42],"derivative":[43,47],"a":[45],"fractional-order":[46],"in":[48,113],"Caputo":[49],"sense.":[50],"Firstly,":[51],"we":[52,94],"discuss":[53],"integral":[56],"properties":[59],"several":[61],"functions":[62],"which":[63,117],"derived":[65],"Mittag-Leffler":[68],"function.":[69],"Secondly,":[70],"using":[72],"homotopy":[74,124],"analysis":[75,125],"method,":[76],"exact":[78,101],"solutions":[79,105],"for":[80,127],"mentioned":[84],"above":[85],"suitable":[87],"initial":[88],"boundary":[89],"conditions":[90],"obtained.":[92],"Finally,":[93],"draw":[95],"computer":[97],"graphics":[98],"solutions,":[102],"approximate":[104],"(truncation":[106],"finite":[108],"terms),":[109],"absolute":[111],"errors":[112],"limited":[115],"area,":[116],"show":[118],"that":[119],"effectiveness":[121],"method":[126],"solving":[128],"equations.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
