{"id":"https://openalex.org/W4200433985","doi":"https://doi.org/10.3390/e23121646","title":"Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense","display_name":"Series Representations for Uncertain Fractional IVPs in the Fuzzy Conformable Fractional Sense","publication_year":2021,"publication_date":"2021-12-07","ids":{"openalex":"https://openalex.org/W4200433985","doi":"https://doi.org/10.3390/e23121646","pmid":"https://pubmed.ncbi.nlm.nih.gov/34945952"},"language":"en","primary_location":{"id":"doi:10.3390/e23121646","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121646","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1646/pdf?version=1640232309","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/23/12/1646/pdf?version=1640232309","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103003993","display_name":"Malik Bataineh","orcid":"https://orcid.org/0000-0002-6313-0203"},"institutions":[{"id":"https://openalex.org/I156983542","display_name":"Jordan University of Science and Technology","ror":"https://ror.org/03y8mtb59","country_code":"JO","type":"education","lineage":["https://openalex.org/I156983542"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Malik Bataineh","raw_affiliation_strings":["Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan"],"raw_orcid":"https://orcid.org/0000-0002-6313-0203","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Jordan University of Science and Technology, Irbid 22110, Jordan","institution_ids":["https://openalex.org/I156983542"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004534298","display_name":"Mohammad Alaroud","orcid":"https://orcid.org/0000-0001-9099-5619"},"institutions":[{"id":"https://openalex.org/I145380033","display_name":"Amman Arab University","ror":"https://ror.org/039xekb14","country_code":"JO","type":"education","lineage":["https://openalex.org/I145380033"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mohammad Alaroud","raw_affiliation_strings":["Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-9099-5619","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Arts and Science, Amman Arab University, Amman 11953, Jordan","institution_ids":["https://openalex.org/I145380033"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042854866","display_name":"Shrideh Al\u2010Omari","orcid":"https://orcid.org/0000-0001-8955-5552"},"institutions":[{"id":"https://openalex.org/I33926330","display_name":"Al-Balqa Applied University","ror":"https://ror.org/00qedmt22","country_code":"JO","type":"education","lineage":["https://openalex.org/I33926330"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Shrideh Al-Omari","raw_affiliation_strings":["Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Basic Sciences, Faculty of Engineering Technology, Al-Balqa Applied University, Amman 11134, Jordan","institution_ids":["https://openalex.org/I33926330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053042789","display_name":"Praveen Agarwal","orcid":"https://orcid.org/0000-0001-7556-8942"},"institutions":[{"id":"https://openalex.org/I4210154633","display_name":"Inspiration Innovation Synergy University","ror":"https://ror.org/04d3d5q14","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210154633"]},{"id":"https://openalex.org/I4401726791","display_name":"Anand International College of Engineering","ror":"https://ror.org/05sy8fj60","country_code":null,"type":"education","lineage":["https://openalex.org/I4401726791"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Praveen Agarwal","raw_affiliation_strings":["Department of Mathematics, Anand International College of Engineering, Jaipur 302012, India"],"raw_orcid":"https://orcid.org/0000-0001-7556-8942","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Anand International College of Engineering, Jaipur 302012, India","institution_ids":["https://openalex.org/I4210154633","https://openalex.org/I4401726791"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5042854866"],"corresponding_institution_ids":["https://openalex.org/I33926330"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":5.1762,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.96767707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"23","issue":"12","first_page":"1646","last_page":"1646"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9988999962806702,"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":0.9711999893188477,"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/residual","display_name":"Residual","score":0.6512874960899353},{"id":"https://openalex.org/keywords/fuzzy-logic","display_name":"Fuzzy logic","score":0.615770161151886},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5709965229034424},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.5682588219642639},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5391535758972168},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.507361114025116},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4657166004180908},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4573395550251007},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4343448579311371},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3669314980506897},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3658595085144043},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2713389992713928},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20752981305122375},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10601890087127686}],"concepts":[{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.6512874960899353},{"id":"https://openalex.org/C58166","wikidata":"https://www.wikidata.org/wiki/Q224821","display_name":"Fuzzy logic","level":2,"score":0.615770161151886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5709965229034424},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5682588219642639},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5391535758972168},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.507361114025116},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4657166004180908},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4573395550251007},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4343448579311371},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3669314980506897},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3658595085144043},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2713389992713928},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20752981305122375},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10601890087127686},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.3390/e23121646","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121646","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1646/pdf?version=1640232309","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},{"id":"pmid:34945952","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34945952","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:doaj.org/article:4505f1439dc64f698dc98aa0a06a1f5d","is_oa":true,"landing_page_url":"https://doaj.org/article/4505f1439dc64f698dc98aa0a06a1f5d","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":"Entropy, Vol 23, Iss 12, p 1646 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/23/12/1646/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e23121646","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":"Entropy; Volume 23; Issue 12; Pages: 1646","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:8700388","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/8700388","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e23121646","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e23121646","pdf_url":"https://www.mdpi.com/1099-4300/23/12/1646/pdf?version=1640232309","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"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":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4200433985.pdf","grobid_xml":"https://content.openalex.org/works/W4200433985.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W1965955764","https://openalex.org/W1980023378","https://openalex.org/W1990950138","https://openalex.org/W1999080212","https://openalex.org/W2032521963","https://openalex.org/W2056258420","https://openalex.org/W2063067239","https://openalex.org/W2070545443","https://openalex.org/W2107477112","https://openalex.org/W2134837756","https://openalex.org/W2301349605","https://openalex.org/W2321307647","https://openalex.org/W2490415376","https://openalex.org/W2519899354","https://openalex.org/W2744957862","https://openalex.org/W2809989124","https://openalex.org/W2897394303","https://openalex.org/W2901508580","https://openalex.org/W2907073664","https://openalex.org/W2913692467","https://openalex.org/W2920237743","https://openalex.org/W2937097319","https://openalex.org/W2979462596","https://openalex.org/W2981336941","https://openalex.org/W2986973281","https://openalex.org/W2990424252","https://openalex.org/W3000253802","https://openalex.org/W3001935612","https://openalex.org/W3002507058","https://openalex.org/W3004959120","https://openalex.org/W3019954140","https://openalex.org/W3031078889","https://openalex.org/W3031334652","https://openalex.org/W3043714792","https://openalex.org/W3082721532","https://openalex.org/W3110664911","https://openalex.org/W3115368248","https://openalex.org/W3141151796","https://openalex.org/W3160523953","https://openalex.org/W3164871107","https://openalex.org/W3166275817","https://openalex.org/W3172290676","https://openalex.org/W3176954771","https://openalex.org/W3195537639","https://openalex.org/W3200072590","https://openalex.org/W3207357751","https://openalex.org/W3207436101","https://openalex.org/W3212572808","https://openalex.org/W4211007335","https://openalex.org/W6752940364","https://openalex.org/W6766909617","https://openalex.org/W6774690748","https://openalex.org/W6803698358","https://openalex.org/W6901805969"],"related_works":["https://openalex.org/W4385420941","https://openalex.org/W2048554683","https://openalex.org/W2026349714","https://openalex.org/W2193374604","https://openalex.org/W1646458645","https://openalex.org/W4206257938","https://openalex.org/W2085058560","https://openalex.org/W2765472174","https://openalex.org/W2015907326","https://openalex.org/W2002676536"],"abstract_inverted_index":{"Fuzzy":[0],"differential":[1,49,77],"equations":[2,92],"provide":[3],"a":[4,65],"crucial":[5],"tool":[6],"for":[7,46,82,110,218],"modeling":[8],"numerous":[9],"phenomena":[10],"and":[11,23,26,60,119,138,173,216],"uncertainties":[12],"that":[13,186,207],"potentially":[14],"arise":[15],"in":[16,98,203,226],"various":[17],"applications":[18],"across":[19],"physics,":[20],"applied":[21],"sciences":[22],"engineering.":[24],"Reliable":[25],"effective":[27],"analytical":[28],"methods":[29],"are":[30,58],"necessary":[31],"to":[32,42,123,194],"obtain":[33,43,124],"the":[34,84,90,111,127,130,136,139,149,163,166,177,181,187,195,200,208,222],"required":[35],"solutions,":[36],"as":[37],"it":[38],"is":[39,168,190,213],"very":[40],"difficult":[41],"accurate":[44,192],"solutions":[45,57,86,109,147,167,220],"certain":[47,54],"fuzzy":[48,55,75,85,150],"equations.":[50,78],"In":[51],"this":[52,204],"paper,":[53],"approximate":[56],"constructed":[59],"analyzed":[61],"by":[62,114,155],"means":[63],"of":[64,74,100,126,129,141,148,162,165,176,221],"residual":[66,104,117,209],"power":[67,105,132,210],"series":[68,106,211],"(RPS)":[69],"technique":[70,212],"involving":[71],"some":[72,171],"class":[73],"fractional":[76,95,116,120,131,151],"The":[79,103,160],"considered":[80],"methodology":[81],"finding":[83],"relies":[87],"on":[88],"converting":[89],"target":[91],"into":[93],"two":[94,157],"crisp":[96],"systems":[97,113],"terms":[99],"\u03c1-cut":[101],"representations.":[102],"therefore":[107],"gives":[108],"converted":[112],"combining":[115],"functions":[118],"Taylor":[121],"expansions":[122],"values":[125],"coefficients":[128],"series.":[133],"To":[134],"validate":[135],"efficiency":[137],"applicability":[140],"our":[142],"proposed":[143,178,188],"approach":[144],"we":[145],"derive":[146],"initial":[152],"value":[153],"problem":[154],"testing":[156],"attractive":[158],"applications.":[159],"compatibility":[161],"behavior":[164],"determined":[169],"via":[170],"graphical":[172],"numerical":[174],"analysis":[175],"results.":[179],"Moreover,":[180],"comparative":[182],"results":[183,201],"point":[184],"out":[185],"method":[189],"more":[191],"compared":[193],"other":[196],"existing":[197],"methods.":[198],"Finally,":[199],"attained":[202],"article":[205],"emphasize":[206],"easy,":[214],"efficient,":[215],"fast":[217],"predicting":[219],"uncertain":[223],"models":[224],"arising":[225],"real":[227],"physical":[228],"phenomena.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":13}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
