{"id":"https://openalex.org/W2906844864","doi":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","title":"Homotopy Analysis Method for the First Order Fuzzy Volterra-Fredholm Integro-differential Equations","display_name":"Homotopy Analysis Method for the First Order Fuzzy Volterra-Fredholm Integro-differential Equations","publication_year":2018,"publication_date":"2018-09-01","ids":{"openalex":"https://openalex.org/W2906844864","doi":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","mag":"2906844864"},"language":"en","primary_location":{"id":"doi:10.11591/ijeecs.v11.i3.pp857-867","doi":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","is_oa":true,"landing_page_url":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","pdf_url":"http://ijeecs.iaescore.com/index.php/IJEECS/article/download/12985/12024","source":{"id":"https://openalex.org/S2764855249","display_name":"Indonesian Journal of Electrical Engineering and Computer Science","issn_l":"2502-4752","issn":["2502-4752","2502-4760"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315009","host_organization_name":"Institute of Advanced Engineering and Science (IAES)","host_organization_lineage":["https://openalex.org/P4310315009"],"host_organization_lineage_names":["Institute of Advanced Engineering and Science (IAES)"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Indonesian Journal of Electrical Engineering and Computer Science","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"http://ijeecs.iaescore.com/index.php/IJEECS/article/download/12985/12024","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058581977","display_name":"Ahmed A. Hamoud","orcid":"https://orcid.org/0000-0002-8877-7337","observed_orcids":["https://orcid.org/0000-0002-8877-7337"]},"institutions":[{"id":"https://openalex.org/I165259314","display_name":"Dr. Babasaheb Ambedkar Marathwada University","ror":"https://ror.org/033pfj584","country_code":"IN","type":"education","lineage":["https://openalex.org/I165259314"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Ahmed A. Hamoud","raw_affiliation_strings":["Dr. Babasaheb Ambedkar Marathwada University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dr. Babasaheb Ambedkar Marathwada University","institution_ids":["https://openalex.org/I165259314"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073279545","display_name":"Kirtiwant P. Ghadle","orcid":"https://orcid.org/0000-0003-3205-5498","observed_orcids":["https://orcid.org/0000-0003-3205-5498"]},"institutions":[{"id":"https://openalex.org/I165259314","display_name":"Dr. Babasaheb Ambedkar Marathwada University","ror":"https://ror.org/033pfj584","country_code":"IN","type":"education","lineage":["https://openalex.org/I165259314"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kirtiwant P. Ghadle","raw_affiliation_strings":["Dr. Babasaheb Ambedkar Marathwada University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dr. Babasaheb Ambedkar Marathwada University","institution_ids":["https://openalex.org/I165259314"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I165259314"],"apc_list":null,"apc_paid":null,"fwci":2.5905,"has_fulltext":true,"cited_by_count":31,"citation_normalized_percentile":{"value":0.92059553,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"11","issue":"3","first_page":"857","last_page":"857"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":1.0,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":9.999999747378752e-05,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.0,"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/homotopy-analysis-method","display_name":"homotopy analysis method","score":0.8970000147819519},{"id":"https://openalex.org/keywords/first-order-integro-differential-equations","display_name":"first-order integro-differential equations","score":0.8320000171661377},{"id":"https://openalex.org/keywords/approximate-solutions","display_name":"approximate solutions","score":0.546999990940094},{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.9409999847412109},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.8489999771118164}],"concepts":[{"id":"https://openalex.org/C173636693","wikidata":"https://www.wikidata.org/wiki/Q17030668","display_name":"Homotopy analysis method","level":3,"score":0.8066716194152832},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7916562557220459},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6852891445159912},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.5893669724464417},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5692122578620911},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.5664249062538147},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5488156676292419},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4759102463722229},{"id":"https://openalex.org/C5961521","wikidata":"https://www.wikidata.org/wiki/Q746083","display_name":"Homotopy","level":2,"score":0.4747205972671509},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.4458073079586029},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4434276521205902},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4056966006755829},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35133737325668335},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18880200386047363},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1146804690361023},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.11591/ijeecs.v11.i3.pp857-867","doi":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","is_oa":true,"landing_page_url":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","pdf_url":"http://ijeecs.iaescore.com/index.php/IJEECS/article/download/12985/12024","source":{"id":"https://openalex.org/S2764855249","display_name":"Indonesian Journal of Electrical Engineering and Computer Science","issn_l":"2502-4752","issn":["2502-4752","2502-4760"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315009","host_organization_name":"Institute of Advanced Engineering and Science (IAES)","host_organization_lineage":["https://openalex.org/P4310315009"],"host_organization_lineage_names":["Institute of Advanced Engineering and Science (IAES)"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Indonesian Journal of Electrical Engineering and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:ojs.www.iaescore.com:article/12985","doi":null,"is_oa":true,"landing_page_url":"http://www.iaescore.com/journals/index.php/IJEECS/article/view/12985","pdf_url":null,"source":{"id":"https://openalex.org/S2764855249","display_name":"Indonesian Journal of Electrical Engineering and Computer Science","issn_l":"2502-4752","issn":["2502-4752","2502-4760"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315009","host_organization_name":"Institute of Advanced Engineering and Science (IAES)","host_organization_lineage":["https://openalex.org/P4310315009"],"host_organization_lineage_names":["Institute of Advanced Engineering and Science (IAES)"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Indonesian Journal of Electrical Engineering and Computer Science; Vol 11, No 3: September 2018; 857-867","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.11591/ijeecs.v11.i3.pp857-867","doi":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","is_oa":true,"landing_page_url":"https://doi.org/10.11591/ijeecs.v11.i3.pp857-867","pdf_url":"http://ijeecs.iaescore.com/index.php/IJEECS/article/download/12985/12024","source":{"id":"https://openalex.org/S2764855249","display_name":"Indonesian Journal of Electrical Engineering and Computer Science","issn_l":"2502-4752","issn":["2502-4752","2502-4760"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":["jufo-1","norway-1","poland-20","russia-white-list-2"],"host_organization":"https://openalex.org/P4310315009","host_organization_name":"Institute of Advanced Engineering and Science (IAES)","host_organization_lineage":["https://openalex.org/P4310315009"],"host_organization_lineage_names":["Institute of Advanced Engineering and Science (IAES)"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Indonesian Journal of Electrical Engineering and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2906844864.pdf","grobid_xml":"https://content.openalex.org/works/W2906844864.grobid-xml"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W604143053","https://openalex.org/W1584611818","https://openalex.org/W1965955764","https://openalex.org/W1969702681","https://openalex.org/W1976196891","https://openalex.org/W1994152317","https://openalex.org/W1999080212","https://openalex.org/W2057434313","https://openalex.org/W2069069851","https://openalex.org/W2084568227","https://openalex.org/W2092092154","https://openalex.org/W2138721505","https://openalex.org/W2149792095","https://openalex.org/W2149890193","https://openalex.org/W2157041604","https://openalex.org/W2337099759","https://openalex.org/W2784600336","https://openalex.org/W2805185890","https://openalex.org/W2892204294","https://openalex.org/W2897327134","https://openalex.org/W2899115415","https://openalex.org/W2903316287","https://openalex.org/W2918952185","https://openalex.org/W2922023551","https://openalex.org/W4254730433"],"related_works":["https://openalex.org/W2362256999","https://openalex.org/W2972080159","https://openalex.org/W2017640945","https://openalex.org/W2031473926","https://openalex.org/W2386739836","https://openalex.org/W2493083010","https://openalex.org/W2021616187","https://openalex.org/W4308895501","https://openalex.org/W22811207","https://openalex.org/W2007245702"],"abstract_inverted_index":{"A":[0],"fuzzy":[1,37],"Volterra-Fredholm":[2],"integro-differential":[3],"equation":[4],"(FVFIDE)":[5],"in":[6],"a":[7],"parametric":[8],"case":[9],"is":[10],"converted":[11],"to":[12,22],"its":[13],"related":[14],"crisp":[15],"case.":[16],"We":[17],"use":[18],"homotopy":[19],"analysis":[20],"method":[21],"find":[23],"the":[24,36,40,52],"approximate":[25],"solution":[26,38],"of":[27,39,51],"this":[28],"system":[29],"and":[30,46,49],"hence":[31],"obtain":[32],"an":[33],"approximation":[34],"for":[35],"FVFIDE.":[41],"This":[42],"paper":[43],"discusses":[44],"existence":[45],"uniqueness":[47],"results":[48],"convergence":[50],"proposed":[53],"method.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":5}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2019-01-11T00:00:00"}