{"id":"https://openalex.org/W4295854289","doi":"https://doi.org/10.3390/axioms11090449","title":"A Swarming Approach for the Novel Second Order Perturbed Pantograph Lane\u2013Emden Model Arising in Astrophysics","display_name":"A Swarming Approach for the Novel Second Order Perturbed Pantograph Lane\u2013Emden Model Arising in Astrophysics","publication_year":2022,"publication_date":"2022-09-02","ids":{"openalex":"https://openalex.org/W4295854289","doi":"https://doi.org/10.3390/axioms11090449"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11090449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090449","pdf_url":"https://www.mdpi.com/2075-1680/11/9/449/pdf?version=1663729531","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/9/449/pdf?version=1663729531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087348734","display_name":"Muneerah Al Nuwairan","orcid":"https://orcid.org/0000-0001-9076-9945"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Muneerah Al Nuwairan","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020317036","display_name":"Zulqurnain Sabir","orcid":"https://orcid.org/0000-0001-7466-6233"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Zulqurnain Sabir","raw_affiliation_strings":["Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Hazara University, Mansehra 21120, Pakistan","institution_ids":["https://openalex.org/I263208278"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087348734"],"corresponding_institution_ids":["https://openalex.org/I4626487"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.2365,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.7543279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"11","issue":"9","first_page":"449","last_page":"449"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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":0.9399999976158142,"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/particle-swarm-optimization","display_name":"Particle swarm optimization","score":0.653531014919281},{"id":"https://openalex.org/keywords/sequential-quadratic-programming","display_name":"Sequential quadratic programming","score":0.574723482131958},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5714048743247986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4780217409133911},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.43114230036735535},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42613059282302856},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4258384108543396},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.37576350569725037},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3576551675796509},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33582356572151184},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19500461220741272}],"concepts":[{"id":"https://openalex.org/C85617194","wikidata":"https://www.wikidata.org/wiki/Q2072794","display_name":"Particle swarm optimization","level":2,"score":0.653531014919281},{"id":"https://openalex.org/C198927703","wikidata":"https://www.wikidata.org/wiki/Q4373881","display_name":"Sequential quadratic programming","level":3,"score":0.574723482131958},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5714048743247986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4780217409133911},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.43114230036735535},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42613059282302856},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4258384108543396},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.37576350569725037},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3576551675796509},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33582356572151184},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19500461220741272},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"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":3,"locations":[{"id":"doi:10.3390/axioms11090449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090449","pdf_url":"https://www.mdpi.com/2075-1680/11/9/449/pdf?version=1663729531","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:60a99964690f48cba97c5d2dcf061e89","is_oa":true,"landing_page_url":"https://doaj.org/article/60a99964690f48cba97c5d2dcf061e89","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 9, p 449 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/9/449/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11090449","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":"Axioms; Volume 11; Issue 9; Pages: 449","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11090449","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090449","pdf_url":"https://www.mdpi.com/2075-1680/11/9/449/pdf?version=1663729531","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4295854289.pdf","grobid_xml":"https://content.openalex.org/works/W4295854289.grobid-xml"},"referenced_works_count":79,"referenced_works":["https://openalex.org/W79873316","https://openalex.org/W1476132770","https://openalex.org/W1623895684","https://openalex.org/W1956057802","https://openalex.org/W1971565872","https://openalex.org/W1986034894","https://openalex.org/W1986347382","https://openalex.org/W1996672882","https://openalex.org/W2021471162","https://openalex.org/W2032092969","https://openalex.org/W2037486322","https://openalex.org/W2043692330","https://openalex.org/W2045250771","https://openalex.org/W2054229934","https://openalex.org/W2054574456","https://openalex.org/W2063670264","https://openalex.org/W2081847801","https://openalex.org/W2105340553","https://openalex.org/W2107453594","https://openalex.org/W2116318141","https://openalex.org/W2141396864","https://openalex.org/W2161502942","https://openalex.org/W2184026024","https://openalex.org/W2201560471","https://openalex.org/W2767749538","https://openalex.org/W2794195850","https://openalex.org/W2798741797","https://openalex.org/W2888707334","https://openalex.org/W2893524191","https://openalex.org/W2906413292","https://openalex.org/W2947137917","https://openalex.org/W2949735065","https://openalex.org/W2954110777","https://openalex.org/W2964454344","https://openalex.org/W2983575492","https://openalex.org/W2987164835","https://openalex.org/W2994551303","https://openalex.org/W2997959082","https://openalex.org/W2999593349","https://openalex.org/W3002359475","https://openalex.org/W3015542020","https://openalex.org/W3017961348","https://openalex.org/W3020127197","https://openalex.org/W3022420077","https://openalex.org/W3023935154","https://openalex.org/W3024566200","https://openalex.org/W3028247906","https://openalex.org/W3032620443","https://openalex.org/W3033568144","https://openalex.org/W3033651060","https://openalex.org/W3034200507","https://openalex.org/W3037285524","https://openalex.org/W3040620092","https://openalex.org/W3041464168","https://openalex.org/W3043215010","https://openalex.org/W3080612479","https://openalex.org/W3085910569","https://openalex.org/W3089074983","https://openalex.org/W3095195965","https://openalex.org/W3107515836","https://openalex.org/W3120514245","https://openalex.org/W3216122690","https://openalex.org/W4200225440","https://openalex.org/W4200464772","https://openalex.org/W4206724665","https://openalex.org/W4210413309","https://openalex.org/W4212955198","https://openalex.org/W4224089554","https://openalex.org/W4281662963","https://openalex.org/W4291144905","https://openalex.org/W4292201143","https://openalex.org/W4292427578","https://openalex.org/W6638374719","https://openalex.org/W6662086378","https://openalex.org/W6664177638","https://openalex.org/W6677111002","https://openalex.org/W6686379669","https://openalex.org/W6764596177","https://openalex.org/W6807081895"],"related_works":["https://openalex.org/W4206704743","https://openalex.org/W4313119266","https://openalex.org/W2164807043","https://openalex.org/W2019128690","https://openalex.org/W4231448069","https://openalex.org/W2128461291","https://openalex.org/W2355907103","https://openalex.org/W2270789747","https://openalex.org/W436931041","https://openalex.org/W1495847109"],"abstract_inverted_index":{"The":[0,30,42,124,150],"purpose":[1],"of":[2,18,27,34,45,85,110,121,126,136,144,155,167,174],"this":[3,46],"study":[4],"is":[5,103,116,129],"to":[6,131],"provide":[7],"a":[8],"mathematical":[9,138],"construction":[10],"based":[11,61,105],"on":[12,62,106],"the":[13,19,24,28,35,51,58,63,75,82,86,94,107,111,119,122,127,137,142,145,156,168,172,175],"novel":[14],"singular":[15,31,54],"perturbed":[16],"model":[17,47,128],"second":[20],"kind":[21],"(NSPM-SK)":[22],"using":[23,50,71,141,163],"standard":[25],"form":[26,109],"Lane\u2013Emden.":[29],"Lane\u2013Emden":[32],"types":[33],"models":[36,66],"have":[37],"abundant":[38],"applications":[39],"in":[40],"astrophysics.":[41],"inclusive":[43],"features":[44],"are":[48,160],"provided":[49,104],"perturbed,":[52],"pantograph,":[53],"point":[55],"together":[56,80,170],"and":[57,93,113,147,153],"shape":[59],"factor":[60],"NSPM-SK.":[64],"These":[65],"become":[67],"more":[68],"complicated":[69],"by":[70,140,162],"these":[72],"factors":[73],"through":[74,118],"artificial":[76],"neural":[77],"networks":[78],"(ANNs)":[79],"with":[81,171],"optimization":[83,90,115,173],"procedures":[84],"swarming":[87],"particle":[88],"swarm":[89],"(PSO)":[91],"paradigms":[92],"local":[95],"sequential":[96],"quadratic":[97],"programming":[98],"(SQP).":[99],"An":[100],"objective":[101],"function":[102],"differential":[108],"NSPM-SK":[112,139],"then":[114],"performed":[117],"hybridization":[120],"PSOSQP.":[123],"exactness":[125],"attained":[130],"solve":[132],"three":[133],"different":[134,164],"variations":[135],"overlapping":[143],"obtained":[146],"true":[148],"results.":[149],"stability,":[151],"robustness,":[152],"convergence":[154],"designed":[157],"numerical":[158],"approach":[159],"perceived":[161],"statistical":[165],"performances":[166],"ANNs":[169],"PSOSQP":[176],"for":[177],"30":[178],"independent":[179],"executions.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}