{"id":"https://openalex.org/W2966665328","doi":"https://doi.org/10.3390/sym11080962","title":"The Solutions of Non-Integer Order Burgers\u2019 Fluid Flowing through a Round Channel with Semi Analytical Technique","display_name":"The Solutions of Non-Integer Order Burgers\u2019 Fluid Flowing through a Round Channel with Semi Analytical Technique","publication_year":2019,"publication_date":"2019-08-01","ids":{"openalex":"https://openalex.org/W2966665328","doi":"https://doi.org/10.3390/sym11080962","mag":"2966665328"},"language":"en","primary_location":{"id":"doi:10.3390/sym11080962","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080962","pdf_url":"https://www.mdpi.com/2073-8994/11/8/962/pdf?version=1564998483","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/2073-8994/11/8/962/pdf?version=1564998483","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"M. Imran","orcid":null},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]},{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Imran","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan","Department of Mathematics, University of Management and Technology Lahore, Punjab 54770, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]},{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology Lahore, Punjab 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041477197","display_name":"Dennis Ling Chuan Ching","orcid":"https://orcid.org/0000-0003-0392-1203"},"institutions":[{"id":"https://openalex.org/I203899302","display_name":"Universiti Teknologi Petronas","ror":"https://ror.org/048g2sh07","country_code":"MY","type":"education","lineage":["https://openalex.org/I203899302"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"D.L.C. Ching","raw_affiliation_strings":["Fundamental and Applied Science Department, Universiti Teknologi Petronas, 32610 Perak, Malaysia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fundamental and Applied Science Department, Universiti Teknologi Petronas, 32610 Perak, Malaysia","institution_ids":["https://openalex.org/I203899302"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022639521","display_name":"Rabia Safdar","orcid":"https://orcid.org/0000-0003-3197-7095"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Rabia Safdar","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011875207","display_name":"Ilyas Khan","orcid":"https://orcid.org/0000-0002-2056-9371"},"institutions":[{"id":"https://openalex.org/I141445968","display_name":"Ton Duc Thang University","ror":"https://ror.org/01drq0835","country_code":"VN","type":"education","lineage":["https://openalex.org/I141445968"]}],"countries":["VN"],"is_corresponding":true,"raw_author_name":"Ilyas Khan","raw_affiliation_strings":["Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam"],"raw_orcid":"https://orcid.org/0000-0002-2056-9371","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 72915, Vietnam","institution_ids":["https://openalex.org/I141445968"]}]},{"author_position":"middle","author":{"id":null,"display_name":"M. Imran","orcid":null},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]},{"id":"https://openalex.org/I87482320","display_name":"University of Management and Technology","ror":"https://ror.org/0095xcq10","country_code":"PK","type":"education","lineage":["https://openalex.org/I87482320"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"M. Imran","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan","Department of Mathematics, University of Management and Technology Lahore, Punjab 54770, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Punjab 38000, Pakistan","institution_ids":["https://openalex.org/I194348271"]},{"raw_affiliation_string":"Department of Mathematics, University of Management and Technology Lahore, Punjab 54770, Pakistan","institution_ids":["https://openalex.org/I87482320"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057525661","display_name":"Kottakkaran Sooppy Nisar","orcid":"https://orcid.org/0000-0001-5769-4320"},"institutions":[{"id":"https://openalex.org/I142608572","display_name":"Prince Sattam Bin Abdulaziz University","ror":"https://ror.org/04jt46d36","country_code":"SA","type":"education","lineage":["https://openalex.org/I142608572"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"K. Nisar","raw_affiliation_strings":["Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5769-4320","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Al-Dawaser 11991, Saudi Arabia","institution_ids":["https://openalex.org/I142608572"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5011875207"],"corresponding_institution_ids":["https://openalex.org/I141445968"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":0.3068,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.52648949,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"11","issue":"8","first_page":"962","last_page":"962"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9968000054359436,"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.8031350374221802},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7942152619361877},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6542559862136841},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5389009714126587},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.5240429043769836},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.5084049105644226},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.49094775319099426},{"id":"https://openalex.org/keywords/fluid-dynamics","display_name":"Fluid dynamics","score":0.48025229573249817},{"id":"https://openalex.org/keywords/inverse-laplace-transform","display_name":"Inverse Laplace transform","score":0.4523783326148987},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.41805315017700195},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.22877630591392517},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21157875657081604},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20978441834449768},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.14140132069587708}],"concepts":[{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.8031350374221802},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7942152619361877},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6542559862136841},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5389009714126587},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.5240429043769836},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5084049105644226},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.49094775319099426},{"id":"https://openalex.org/C90278072","wikidata":"https://www.wikidata.org/wiki/Q216320","display_name":"Fluid dynamics","level":2,"score":0.48025229573249817},{"id":"https://openalex.org/C60455284","wikidata":"https://www.wikidata.org/wiki/Q2162701","display_name":"Inverse Laplace transform","level":3,"score":0.4523783326148987},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.41805315017700195},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.22877630591392517},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21157875657081604},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20978441834449768},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.14140132069587708},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11080962","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080962","pdf_url":"https://www.mdpi.com/2073-8994/11/8/962/pdf?version=1564998483","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:f965ea04bfa8400c840d03b47122541f","is_oa":true,"landing_page_url":"https://doaj.org/article/f965ea04bfa8400c840d03b47122541f","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 11, Iss 8, p 962 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11080962","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11080962","pdf_url":"https://www.mdpi.com/2073-8994/11/8/962/pdf?version=1564998483","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W582640803","https://openalex.org/W1523147982","https://openalex.org/W1607904336","https://openalex.org/W1975372873","https://openalex.org/W1985043228","https://openalex.org/W1993169582","https://openalex.org/W2004497270","https://openalex.org/W2004755618","https://openalex.org/W2005841504","https://openalex.org/W2015571768","https://openalex.org/W2019606567","https://openalex.org/W2034790565","https://openalex.org/W2049519712","https://openalex.org/W2057342974","https://openalex.org/W2067757814","https://openalex.org/W2076005793","https://openalex.org/W2080455786","https://openalex.org/W2082519630","https://openalex.org/W2084261994","https://openalex.org/W2089444942","https://openalex.org/W2090625297","https://openalex.org/W2093275073","https://openalex.org/W2095125002","https://openalex.org/W2320094268","https://openalex.org/W2580629604","https://openalex.org/W2611735158","https://openalex.org/W2787959293","https://openalex.org/W2905447296","https://openalex.org/W3140511778","https://openalex.org/W6658233682","https://openalex.org/W6757392414"],"related_works":["https://openalex.org/W3022275705","https://openalex.org/W193874820","https://openalex.org/W1996624184","https://openalex.org/W2328813089","https://openalex.org/W3021788336","https://openalex.org/W2504967562","https://openalex.org/W2260908168","https://openalex.org/W3023736802","https://openalex.org/W3116142293","https://openalex.org/W4309989447"],"abstract_inverted_index":{"The":[0,91,118],"solutions":[1,94],"for":[2,19],"velocity":[3,59],"and":[4,15,44,88,105,124,130],"stress":[5],"are":[6,108,127],"derived":[7],"by":[8,85,133],"using":[9],"the":[10,20,35,51,55,71,78,96,99,111,121],"methods":[11],"of":[12,23,50,54,73,76,98,103,114,120],"Laplace":[13,80],"transformation":[14],"Modified":[16,100],"Bessel\u2019s":[17,101],"equation":[18],"rotational":[21],"flow":[22,47],"Burgers\u2019":[24],"fluid":[25,36,46],"flowing":[26],"through":[27],"an":[28],"unbounded":[29],"round":[30],"channel.":[31],"Initially,":[32],"supposed":[33],"that":[34],"is":[37,48,82],"not":[38],"moving":[39],"with":[40,58,64],"t":[41,62],"=":[42],"0":[43],"afterward":[45],"because":[49],"circular":[52],"motion":[53],"around":[56],"channel":[57],"\u03a9":[60],"R":[61],"p":[63],"time":[65],"positively":[66],"grater":[67],"than":[68],"zero.":[69],"At":[70],"point":[72],"complicated":[74],"expressions":[75],"results,":[77],"inverse":[79],"transform":[81],"alternately":[83],"calculated":[84],"\u201cStehfest\u2019s":[86],"algorithm\u201d":[87],"\u201cMATHCAD\u201d":[89],"numerically.":[90],"numerically":[92],"obtained":[93],"in":[95],"terms":[97],"equations":[102],"first":[104],"second":[106],"kind,":[107],"satisfying":[109],"all":[110],"imposed":[112],"conditions":[113],"given":[115],"mathematical":[116],"model.":[117],"impact":[119],"various":[122],"physical":[123],"fractional":[125],"parameters":[126],"also":[128],"indeed":[129],"so":[131],"presented":[132],"graphical":[134],"demonstrations.":[135]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
