{"id":"https://openalex.org/W4408373645","doi":"https://doi.org/10.3390/sym17030423","title":"Loss of Exponential Stability for a Delayed Timoshenko System Symmetrically in Both Viscoelasticity and Fractional Boundary Controls","display_name":"Loss of Exponential Stability for a Delayed Timoshenko System Symmetrically in Both Viscoelasticity and Fractional Boundary Controls","publication_year":2025,"publication_date":"2025-03-12","ids":{"openalex":"https://openalex.org/W4408373645","doi":"https://doi.org/10.3390/sym17030423"},"language":"en","primary_location":{"id":"doi:10.3390/sym17030423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030423","pdf_url":"https://www.mdpi.com/2073-8994/17/3/423/pdf?version=1741768325","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"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/17/3/423/pdf?version=1741768325","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5116599824","display_name":"Mokhtaria Bouariba Sadoun","orcid":null},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]}],"countries":["DZ"],"is_corresponding":true,"raw_author_name":"Mokhtaria Bouariba Sadoun","raw_affiliation_strings":["Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria","institution_ids":["https://openalex.org/I233209018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031168643","display_name":"Amine Benaissa Cherif","orcid":null},"institutions":[{"id":"https://openalex.org/I3124969661","display_name":"Universit\u00e9 des Sciences et de la Technologie d'Oran Mohamed Boudiaf","ror":"https://ror.org/02nbj1r55","country_code":"DZ","type":"education","lineage":["https://openalex.org/I3124969661"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Amine Benaissa Cherif","raw_affiliation_strings":["Department of Mathematics, University of Sciences and Technology Oran Mohamed Boudiaf, Oran 31000, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Sciences and Technology Oran Mohamed Boudiaf, Oran 31000, Algeria","institution_ids":["https://openalex.org/I3124969661"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018046679","display_name":"Rachid Bentifour","orcid":"https://orcid.org/0000-0003-3177-663X"},"institutions":[{"id":"https://openalex.org/I233209018","display_name":"University of Abou Bekr Belka\u00efd","ror":"https://ror.org/00jsjm362","country_code":"DZ","type":"education","lineage":["https://openalex.org/I233209018"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Rachid Bentifour","raw_affiliation_strings":["Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Abou Bekr Belkaid, Tlemcen 13000, Algeria","institution_ids":["https://openalex.org/I233209018"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060768113","display_name":"Keltoum Bouhali","orcid":"https://orcid.org/0000-0002-3561-6353"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Keltoum Bouhali","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5038025404","display_name":"Mohamed Biomy","orcid":"https://orcid.org/0000-0002-6769-0881"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]},{"id":"https://openalex.org/I4210165529","display_name":"University of Business and Technology","ror":"https://ror.org/05tcr1n44","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210165529"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohamed Biomy","raw_affiliation_strings":["Department of Management Information Systems, College of Business Administration, Qassim University, Buraydah 52571, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Management Information Systems, College of Business Administration, Qassim University, Buraydah 52571, Saudi Arabia","institution_ids":["https://openalex.org/I4210165529","https://openalex.org/I156216236"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073467481","display_name":"Khaled Zennir","orcid":"https://orcid.org/0000-0002-7895-4168"},"institutions":[{"id":"https://openalex.org/I156216236","display_name":"Qassim University","ror":"https://ror.org/01wsfe280","country_code":"SA","type":"education","lineage":["https://openalex.org/I156216236"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khaled Zennir","raw_affiliation_strings":["Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia","institution_ids":["https://openalex.org/I156216236"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5116599824"],"corresponding_institution_ids":["https://openalex.org/I233209018"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.4317,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.87206914,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":96},"biblio":{"volume":"17","issue":"3","first_page":"423","last_page":"423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/T11416","display_name":"Numerical methods for differential equations","score":0.996399998664856,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9955000281333923,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.657765805721283},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.5825545787811279},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.555172860622406},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5312703847885132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5085991621017456},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.491690456867218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.46583452820777893},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.41276732087135315},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3112263083457947},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18016424775123596},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.09699690341949463},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.09028875827789307}],"concepts":[{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.657765805721283},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.5825545787811279},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.555172860622406},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5312703847885132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5085991621017456},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.491690456867218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.46583452820777893},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.41276732087135315},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3112263083457947},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18016424775123596},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.09699690341949463},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.09028875827789307},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/sym17030423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030423","pdf_url":"https://www.mdpi.com/2073-8994/17/3/423/pdf?version=1741768325","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"}],"best_oa_location":{"id":"doi:10.3390/sym17030423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym17030423","pdf_url":"https://www.mdpi.com/2073-8994/17/3/423/pdf?version=1741768325","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":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4408373645.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W1974603761","https://openalex.org/W1986228928","https://openalex.org/W1997593775","https://openalex.org/W1999444653","https://openalex.org/W2029298098","https://openalex.org/W2038645584","https://openalex.org/W2042649373","https://openalex.org/W2060147468","https://openalex.org/W2123138835","https://openalex.org/W2918659403","https://openalex.org/W2985512975","https://openalex.org/W3126179768","https://openalex.org/W3130134441","https://openalex.org/W4200487474","https://openalex.org/W4210530405","https://openalex.org/W4285809227","https://openalex.org/W4387400013","https://openalex.org/W6805373281"],"related_works":["https://openalex.org/W4221057967","https://openalex.org/W4243019676","https://openalex.org/W2517352629","https://openalex.org/W2783562378","https://openalex.org/W4293192718","https://openalex.org/W4394391585","https://openalex.org/W2045876794","https://openalex.org/W2255703620","https://openalex.org/W807319463","https://openalex.org/W2040929039"],"abstract_inverted_index":{"The":[0,45],"stability":[1,60,69,101,108],"analysis":[2],"of":[3,18,23,33,70,99],"Timoshenko":[4,78],"beam":[5],"systems":[6],"that":[7],"incorporate":[8],"delays":[9],"and":[10,37,61,86,106],"fractional":[11,39,83,87],"boundary":[12,38,88],"controls":[13],"is":[14,47],"a":[15,42,50,77],"complex":[16],"area":[17],"study":[19,26,67],"in":[20,41,75,80],"the":[21,30,58,68,95,97],"field":[22],"viscoelasticity.":[24],"Our":[25],"aims":[27],"to":[28,48,57],"balance":[29],"symmetric":[31],"influence":[32],"internal":[34],"viscoelastic":[35],"damping":[36,40],"structured":[43],"way.":[44],"goal":[46],"establish":[49],"system":[51,79],"where":[52],"both":[53],"effects":[54],"contribute":[55],"symmetrically":[56],"overall":[59],"dynamics.":[62],"In":[63],"this":[64],"paper,":[65],"we":[66],"certain":[71],"hyperbolic":[72],"evolution":[73],"problems,":[74],"particular,":[76],"viscoelasticity":[81],"with":[82],"time":[84],"delay":[85],"controls.":[89],"We":[90],"prove,":[91],"under":[92],"assumptions":[93],"on":[94],"data,":[96],"lack":[98],"exponential":[100],"decay":[102,109],"rate":[103,110],"when":[104,111],"\u03b7\u22650":[105],"polynomial":[107],"\u03b7&gt;0":[112],"using":[113],"energy":[114],"methods.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
