{"id":"https://openalex.org/W4309309650","doi":"https://doi.org/10.3390/sym14112424","title":"Freelance Model with Atangana\u2013Baleanu Caputo Fractional Derivative","display_name":"Freelance Model with Atangana\u2013Baleanu Caputo Fractional Derivative","publication_year":2022,"publication_date":"2022-11-16","ids":{"openalex":"https://openalex.org/W4309309650","doi":"https://doi.org/10.3390/sym14112424"},"language":"en","primary_location":{"id":"doi:10.3390/sym14112424","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112424","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2424/pdf?version=1668573980","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/11/2424/pdf?version=1668573980","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061499682","display_name":"Fareeha Sami Khan","orcid":"https://orcid.org/0000-0002-4766-028X"},"institutions":[{"id":"https://openalex.org/I40597779","display_name":"Federal Urdu University","ror":"https://ror.org/02b52th27","country_code":"PK","type":"education","lineage":["https://openalex.org/I40597779"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Fareeha Sami Khan","raw_affiliation_strings":["Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-4766-028X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan","institution_ids":["https://openalex.org/I40597779"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074574938","display_name":"Muhammad Khalid","orcid":"https://orcid.org/0000-0002-5233-6505"},"institutions":[{"id":"https://openalex.org/I40597779","display_name":"Federal Urdu University","ror":"https://ror.org/02b52th27","country_code":"PK","type":"education","lineage":["https://openalex.org/I40597779"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Khalid","raw_affiliation_strings":["Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5233-6505","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Federal Urdu University of Arts, Science & Technology, Karachi 75300, Pakistan","institution_ids":["https://openalex.org/I40597779"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076617733","display_name":"Areej A. Almoneef","orcid":"https://orcid.org/0000-0001-7041-3730"},"institutions":[{"id":"https://openalex.org/I106778892","display_name":"Princess Nourah bint Abdulrahman University","ror":"https://ror.org/05b0cyh02","country_code":"SA","type":"education","lineage":["https://openalex.org/I106778892"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Areej A. Al-moneef","raw_affiliation_strings":["Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia","institution_ids":["https://openalex.org/I106778892"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015791655","display_name":"Ali Hasan Ali","orcid":"https://orcid.org/0000-0003-2959-4212"},"institutions":[{"id":"https://openalex.org/I126633494","display_name":"University of Basrah","ror":"https://ror.org/00840ea57","country_code":"IQ","type":"education","lineage":["https://openalex.org/I126633494"]},{"id":"https://openalex.org/I132735039","display_name":"University of Debrecen","ror":"https://ror.org/02xf66n48","country_code":"HU","type":"education","lineage":["https://openalex.org/I132735039"]}],"countries":["HU","IQ"],"is_corresponding":false,"raw_author_name":"Ali Hasan Ali","raw_affiliation_strings":["Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq","Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary"],"raw_orcid":"https://orcid.org/0000-0003-2959-4212","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq","institution_ids":["https://openalex.org/I126633494"]},{"raw_affiliation_string":"Institute of Mathematics, University of Debrecen, Pf. 400, H-4002 Debrecen, Hungary","institution_ids":["https://openalex.org/I132735039"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034511816","display_name":"Omar Bazighifan","orcid":"https://orcid.org/0000-0002-7251-9608"},"institutions":[{"id":"https://openalex.org/I319841309","display_name":"Hadhramout University","ror":"https://ror.org/02kv0px94","country_code":"YE","type":"education","lineage":["https://openalex.org/I319841309"]},{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]},{"id":"https://openalex.org/I4405263500","display_name":"Seiyun University","ror":"https://ror.org/01xp8dp03","country_code":"YE","type":"education","lineage":["https://openalex.org/I4405263500"]}],"countries":["IT","YE"],"is_corresponding":true,"raw_author_name":"Omar Bazighifan","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen","Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen","Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7251-9608","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Seiyun University, Hadhramout 50512, Yemen","institution_ids":["https://openalex.org/I4405263500"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen","institution_ids":["https://openalex.org/I319841309"]},{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":6,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5034511816"],"corresponding_institution_ids":["https://openalex.org/I319841309","https://openalex.org/I4210155399","https://openalex.org/I4405263500"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.304,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.88630077,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"14","issue":"11","first_page":"2424","last_page":"2424"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9865999817848206,"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"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9689000248908997,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.8017427921295166},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6875576972961426},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5424339175224304},{"id":"https://openalex.org/keywords/fixed-point-theorem","display_name":"Fixed-point theorem","score":0.5384888648986816},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5154493451118469},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38567039370536804},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3344349265098572},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3257264494895935},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21775329113006592}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.8017427921295166},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6875576972961426},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5424339175224304},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.5384888648986816},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5154493451118469},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38567039370536804},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3344349265098572},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3257264494895935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21775329113006592}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14112424","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112424","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2424/pdf?version=1668573980","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1463701b42cd4fe790e3d60976d658ec","is_oa":true,"landing_page_url":"https://doaj.org/article/1463701b42cd4fe790e3d60976d658ec","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 11, p 2424 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/11/2424/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14112424","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14112424","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14112424","pdf_url":"https://www.mdpi.com/2073-8994/14/11/2424/pdf?version=1668573980","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/9","score":0.4099999964237213,"display_name":"Industry, innovation and infrastructure"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309309650.pdf","grobid_xml":"https://content.openalex.org/works/W4309309650.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W592802322","https://openalex.org/W1972551677","https://openalex.org/W2145401214","https://openalex.org/W2251268089","https://openalex.org/W2382056600","https://openalex.org/W2403548919","https://openalex.org/W2556784265","https://openalex.org/W2963641381","https://openalex.org/W2990310869","https://openalex.org/W3014161171","https://openalex.org/W3107593160","https://openalex.org/W3125410844","https://openalex.org/W3200187276","https://openalex.org/W3203206800","https://openalex.org/W4281550816","https://openalex.org/W4283069910","https://openalex.org/W4285138316","https://openalex.org/W4295969966","https://openalex.org/W6713389019","https://openalex.org/W6730176618","https://openalex.org/W6770067534","https://openalex.org/W6979976599"],"related_works":["https://openalex.org/W571281153","https://openalex.org/W2949403936","https://openalex.org/W4301247218","https://openalex.org/W3023806604","https://openalex.org/W2952139525","https://openalex.org/W2129818458","https://openalex.org/W4289551052","https://openalex.org/W2340777379","https://openalex.org/W4390756076","https://openalex.org/W4243074410"],"abstract_inverted_index":{"As":[0],"technology":[1],"advances":[2],"and":[3,40,60,77,99],"the":[4,17,35,41,58,63,73,89,95,104],"Internet":[5],"makes":[6],"our":[7],"world":[8],"a":[9],"global":[10],"village,":[11],"it":[12],"is":[13,28,54,70],"important":[14],"to":[15,33,56,102],"understand":[16],"prospective":[18],"career":[19],"of":[20,38,43,62,106],"freelancing.":[21],"A":[22],"novel":[23],"symmetric":[24],"fractional":[25,64,74],"mathematical":[26],"model":[27,98],"introduced":[29],"in":[30,45],"this":[31,49,107],"study":[32],"describe":[34],"competitive":[36],"market":[37],"freelancing":[39],"significance":[42],"information":[44],"its":[46],"acceptance.":[47],"In":[48],"study,":[50],"fixed":[51],"point":[52],"theory":[53],"applied":[55],"analyze":[57],"uniqueness":[59],"existence":[61],"freelance":[65,97],"model.":[66,108],"Its":[67],"numerical":[68],"solution":[69],"derived":[71],"using":[72],"Euler\u2019s":[75],"method,":[76],"each":[78],"case":[79],"has":[80],"been":[81,92],"presented":[82],"graphically":[83],"as":[84,86],"well":[85],"tabular.":[87],"Further,":[88],"results":[90],"have":[91],"compared":[93],"with":[94],"classic":[96],"real":[100],"data":[101],"show":[103],"importance":[105]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":9}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2022-11-26T00:00:00"}
