{"id":"https://openalex.org/W2931053822","doi":"https://doi.org/10.3390/sym11040449","title":"Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo\u2013Fabrizio Derivative","display_name":"Unsteady Flow of Fractional Fluid between Two Parallel Walls with Arbitrary Wall Shear Stress Using Caputo\u2013Fabrizio Derivative","publication_year":2019,"publication_date":"2019-04-01","ids":{"openalex":"https://openalex.org/W2931053822","doi":"https://doi.org/10.3390/sym11040449","mag":"2931053822"},"language":"en","primary_location":{"id":"doi:10.3390/sym11040449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040449","pdf_url":"https://www.mdpi.com/2073-8994/11/4/449/pdf?version=1554104745","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/2073-8994/11/4/449/pdf?version=1554104745","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5114593972","display_name":"Muhammad Asif","orcid":"https://orcid.org/0000-0003-0178-9659"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Asif","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-0178-9659","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000830883","display_name":"Sami Ul Haq","orcid":"https://orcid.org/0000-0001-6260-8407"},"institutions":[{"id":"https://openalex.org/I206573129","display_name":"Islamia College University","ror":"https://ror.org/02p2c1595","country_code":"PK","type":"education","lineage":["https://openalex.org/I206573129"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sami Ul Haq","raw_affiliation_strings":["Department of Mathematics, Islamia College University, Peshawar 25000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Islamia College University, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I206573129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040226905","display_name":"Saeed Islam","orcid":"https://orcid.org/0000-0001-5263-4871"},"institutions":[{"id":"https://openalex.org/I181063083","display_name":"Abdul Wali Khan University Mardan","ror":"https://ror.org/03b9y4e65","country_code":"PK","type":"education","lineage":["https://openalex.org/I181063083"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saeed Islam","raw_affiliation_strings":["Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan","institution_ids":["https://openalex.org/I181063083"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102715200","display_name":"Tawfeeq Abdullah Alkanhal","orcid":"https://orcid.org/0000-0003-1825-6605"},"institutions":[{"id":"https://openalex.org/I195631090","display_name":"Majmaah University","ror":"https://ror.org/01mcrnj60","country_code":"SA","type":"education","lineage":["https://openalex.org/I195631090"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Tawfeeq Abdullah Alkanhal","raw_affiliation_strings":["Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Majmaah 11952, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0002-2056-9371","affiliations":[{"raw_affiliation_string":"Department of Mechatronics and System Engineering, College of Engineering, Majmaah University, Majmaah 11952, Saudi Arabia","institution_ids":["https://openalex.org/I195631090"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5107898896","display_name":"Zar Ali Khan","orcid":null},"institutions":[{"id":"https://openalex.org/I36001604","display_name":"University of Peshawar","ror":"https://ror.org/02t2qwf81","country_code":"PK","type":"education","lineage":["https://openalex.org/I36001604"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zar Ali Khan","raw_affiliation_strings":["Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I36001604"]}]},{"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":"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":"Kottakkaran Sooppy 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":3,"institutions_distinct_count":6,"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":1.1248,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.75525447,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"449","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11379","display_name":"Rheology and Fluid Dynamics Studies","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/1507","display_name":"Fluid Flow and Transfer Processes"},"field":{"id":"https://openalex.org/fields/15","display_name":"Chemical Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7265370488166809},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7061579823493958},{"id":"https://openalex.org/keywords/shear-stress","display_name":"Shear stress","score":0.5971085429191589},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.5845076441764832},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.4895678460597992},{"id":"https://openalex.org/keywords/shear","display_name":"Shear (geology)","score":0.4753054082393646},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4648147523403168},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46178749203681946},{"id":"https://openalex.org/keywords/shear-flow","display_name":"Shear flow","score":0.4493747055530548},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.43311983346939087},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3595409393310547},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.17048469185829163},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.08337682485580444},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.06675183773040771}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7265370488166809},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7061579823493958},{"id":"https://openalex.org/C21141959","wikidata":"https://www.wikidata.org/wiki/Q657936","display_name":"Shear stress","level":2,"score":0.5971085429191589},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.5845076441764832},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.4895678460597992},{"id":"https://openalex.org/C96035792","wikidata":"https://www.wikidata.org/wiki/Q43606218","display_name":"Shear (geology)","level":2,"score":0.4753054082393646},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4648147523403168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46178749203681946},{"id":"https://openalex.org/C135768490","wikidata":"https://www.wikidata.org/wiki/Q2250602","display_name":"Shear flow","level":2,"score":0.4493747055530548},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.43311983346939087},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3595409393310547},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.17048469185829163},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.08337682485580444},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.06675183773040771},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11040449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040449","pdf_url":"https://www.mdpi.com/2073-8994/11/4/449/pdf?version=1554104745","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:716b2c5b1387487dacc1520f443046f5","is_oa":true,"landing_page_url":"https://doaj.org/article/716b2c5b1387487dacc1520f443046f5","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 4, p 449 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11040449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11040449","pdf_url":"https://www.mdpi.com/2073-8994/11/4/449/pdf?version=1554104745","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":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2931053822.pdf","grobid_xml":"https://content.openalex.org/works/W2931053822.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W197255007","https://openalex.org/W1963563982","https://openalex.org/W1967229517","https://openalex.org/W2010179765","https://openalex.org/W2020038537","https://openalex.org/W2047510778","https://openalex.org/W2071617928","https://openalex.org/W2078643611","https://openalex.org/W2083559699","https://openalex.org/W2089904505","https://openalex.org/W2147105743","https://openalex.org/W2157452532","https://openalex.org/W2207710677","https://openalex.org/W2259227674","https://openalex.org/W2288961399","https://openalex.org/W2316819747","https://openalex.org/W2344744673","https://openalex.org/W2480455111","https://openalex.org/W2556784265","https://openalex.org/W2740460687","https://openalex.org/W2758898451","https://openalex.org/W2779153382","https://openalex.org/W2789088221","https://openalex.org/W2790210339","https://openalex.org/W2791636236","https://openalex.org/W2791757467","https://openalex.org/W4236165936","https://openalex.org/W6662510157","https://openalex.org/W6730176618","https://openalex.org/W6749452370"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W3148881609","https://openalex.org/W4317627639","https://openalex.org/W4313396013","https://openalex.org/W3024206168","https://openalex.org/W3005643231","https://openalex.org/W2806181810","https://openalex.org/W2310382154"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"unidirectional":[3],"flows":[4],"of":[5,28,41,65,73,105],"fractional":[6,75,85],"viscous":[7,108],"fluids":[8],"in":[9,67],"a":[10,35,92,106],"rectangular":[11],"channel":[12,103],"are":[13,119,147],"studied.":[14],"The":[15,31,110,145],"flow":[16,104],"is":[17],"generated":[18],"by":[19,45,56,121],"the":[20,25,29,39,46,58,62,68,74,102],"shear":[21,117,140],"stress":[22,118],"given":[23],"on":[24,38],"bottom":[26],"plate":[27],"channel.":[30],"authors":[32,51],"have":[33,52,79,90],"developed":[34,91],"generalized":[36,86,107],"model":[37,94],"basis":[40],"constitutive":[42,87],"equations":[43],"described":[44],"time-fractional":[47,59],"Caputo\u2013Fabrizio":[48],"derivative.":[49],"Many":[50],"published":[53],"different":[54,131],"results":[55,146],"applying":[57],"derivative":[60],"to":[61,95,101],"local":[63],"part":[64],"acceleration":[66],"momentum":[69],"equation.":[70],"This":[71],"approach":[72],"models":[76],"does":[77],"not":[78],"sufficient":[80],"physical":[81],"background.":[82],"By":[83],"using":[84,122],"equations,":[88],"we":[89],"proper":[93],"investigate":[96],"exact":[97,111],"analytical":[98],"solutions":[99,112],"corresponding":[100],"fluid.":[109],"for":[113,129],"velocity":[114],"field":[115],"and":[116,125,141,149],"obtained":[120],"Laplace":[123],"transform":[124],"Fourier":[126],"integral":[127],"transformation,":[128],"three":[130],"cases":[132],"namely":[133],"(i)":[134],"constant":[135],"shear,":[136],"(ii)":[137],"ramped":[138],"type":[139],"(iii)":[142],"oscillating":[143],"shear.":[144],"plotted":[148],"discussed.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
