{"id":"https://openalex.org/W4390788778","doi":"https://doi.org/10.3390/computation12010014","title":"Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators","display_name":"Cutting-Edge Computational Approaches for Approximating Nonlocal Variable-Order Operators","publication_year":2024,"publication_date":"2024-01-12","ids":{"openalex":"https://openalex.org/W4390788778","doi":"https://doi.org/10.3390/computation12010014"},"language":"en","primary_location":{"id":"doi:10.3390/computation12010014","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010014","pdf_url":"https://www.mdpi.com/2079-3197/12/1/14/pdf?version=1705475134","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/12/1/14/pdf?version=1705475134","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093679307","display_name":"Nayereh Tanha","orcid":null},"institutions":[{"id":"https://openalex.org/I33162209","display_name":"Islamic Azad University, Lahijan Branch","ror":"https://ror.org/03dhqyc75","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I33162209"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Nayereh Tanha","raw_affiliation_strings":["Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran","Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran","institution_ids":["https://openalex.org/I33162209"]},{"raw_affiliation_string":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran;","institution_ids":["https://openalex.org/I33162209"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077062428","display_name":"Behrouz Parsa Moghaddam","orcid":"https://orcid.org/0000-0003-4957-9028"},"institutions":[{"id":"https://openalex.org/I33162209","display_name":"Islamic Azad University, Lahijan Branch","ror":"https://ror.org/03dhqyc75","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I33162209"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Behrouz Parsa Moghaddam","raw_affiliation_strings":["Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran","Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran","institution_ids":["https://openalex.org/I33162209"]},{"raw_affiliation_string":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 1616, Iran;","institution_ids":["https://openalex.org/I33162209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067730176","display_name":"Mousa Ilie","orcid":"https://orcid.org/0000-0002-1165-8815"},"institutions":[{"id":"https://openalex.org/I4210098966","display_name":"Islamic Azad University Rasht Branch","ror":"https://ror.org/0151gh112","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210098966"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Mousa Ilie","raw_affiliation_strings":["Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. Box 3516-41335, Iran","Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. Box 3516-41335, Iran;"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. Box 3516-41335, Iran","institution_ids":["https://openalex.org/I4210098966"]},{"raw_affiliation_string":"Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht P.O. Box 3516-41335, Iran;","institution_ids":["https://openalex.org/I4210098966"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5093679307"],"corresponding_institution_ids":["https://openalex.org/I33162209"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.4123,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50890089,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"12","issue":"1","first_page":"14","last_page":"14"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9980000257492065,"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/T10514","display_name":"Numerical methods in engineering","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/variable","display_name":"Variable (mathematics)","score":0.7337401509284973},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.5924020409584045},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5562611818313599},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47877466678619385},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47661176323890686},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4693164825439453},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.434287428855896},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4270560145378113},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.413130521774292},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.40117841958999634},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.19125568866729736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11404773592948914},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.10834240913391113},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.08554229140281677}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7337401509284973},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.5924020409584045},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5562611818313599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47877466678619385},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47661176323890686},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4693164825439453},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.434287428855896},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4270560145378113},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.413130521774292},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40117841958999634},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.19125568866729736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11404773592948914},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.10834240913391113},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.08554229140281677},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/computation12010014","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010014","pdf_url":"https://www.mdpi.com/2079-3197/12/1/14/pdf?version=1705475134","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:23fb760c7ecc4adab527fd3ee2dfbb52","is_oa":true,"landing_page_url":"https://doaj.org/article/23fb760c7ecc4adab527fd3ee2dfbb52","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":"Computation, Vol 12, Iss 1, p 14 (2024)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2079-3197/12/1/14/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/computation12010014","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":"Computation","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/computation12010014","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation12010014","pdf_url":"https://www.mdpi.com/2079-3197/12/1/14/pdf?version=1705475134","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"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":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4390788778.pdf","grobid_xml":"https://content.openalex.org/works/W4390788778.grobid-xml"},"referenced_works_count":46,"referenced_works":["https://openalex.org/W1775511988","https://openalex.org/W1972646390","https://openalex.org/W1980857788","https://openalex.org/W1989974108","https://openalex.org/W2017663693","https://openalex.org/W2024592722","https://openalex.org/W2048407387","https://openalex.org/W2064466939","https://openalex.org/W2088706360","https://openalex.org/W2109367300","https://openalex.org/W2277623713","https://openalex.org/W2567155074","https://openalex.org/W2590249405","https://openalex.org/W2595699904","https://openalex.org/W2604906738","https://openalex.org/W2772500265","https://openalex.org/W2789907329","https://openalex.org/W2820513219","https://openalex.org/W2923505959","https://openalex.org/W2979169247","https://openalex.org/W2999451223","https://openalex.org/W3038052830","https://openalex.org/W3048831613","https://openalex.org/W3110001612","https://openalex.org/W3161559858","https://openalex.org/W3184892795","https://openalex.org/W3210758412","https://openalex.org/W4206116562","https://openalex.org/W4223931696","https://openalex.org/W4226337015","https://openalex.org/W4226389477","https://openalex.org/W4283020484","https://openalex.org/W4362468004","https://openalex.org/W4368617430","https://openalex.org/W4380683322","https://openalex.org/W4381665988","https://openalex.org/W4382722246","https://openalex.org/W4388977958","https://openalex.org/W6638164242","https://openalex.org/W6643501911","https://openalex.org/W6645452765","https://openalex.org/W6662828409","https://openalex.org/W6666847327","https://openalex.org/W6753131963","https://openalex.org/W6799117754","https://openalex.org/W6852328675"],"related_works":["https://openalex.org/W3093584180","https://openalex.org/W2551845725","https://openalex.org/W2045588195","https://openalex.org/W3018365851","https://openalex.org/W3207484021","https://openalex.org/W2052899165","https://openalex.org/W2082153974","https://openalex.org/W2160477533","https://openalex.org/W2122776646","https://openalex.org/W2008562718"],"abstract_inverted_index":{"This":[0],"study":[1,98],"presents":[2],"an":[3],"algorithmically":[4],"efficient":[5],"approach":[6,50],"to":[7,28,109,127,134,143],"address":[8],"the":[9,45,64,88,101,114,135,144],"complexities":[10],"associated":[11,137],"with":[12,51,138],"nonlocal":[13,70,139],"variable-order":[14,71,106,140],"operators":[15],"characterized":[16],"by":[17,92],"diverse":[18],"definitions.":[19],"The":[20,75],"proposed":[21],"method":[22],"employs":[23],"integro":[24],"spline":[25],"quasi":[26],"interpolation":[27],"approximate":[29],"these":[30],"operators,":[31,141],"aiming":[32],"for":[33,68],"enhanced":[34],"accuracy":[35],"and":[36,59,73,131],"computational":[37],"efficiency.":[38],"We":[39],"conduct":[40],"a":[41,84,110,118,129],"thorough":[42],"comparison":[43],"of":[44,87,103,113,120],"outcomes":[46],"obtained":[47],"through":[48],"this":[49,80,97,124],"other":[52],"established":[53],"techniques,":[54],"including":[55],"finite":[56],"difference,":[57],"IQS,":[58],"B-spline":[60],"methods,":[61],"documented":[62],"in":[63,79],"applied":[65,145],"mathematics":[66,146],"literature":[67],"handling":[69],"derivatives":[72],"integrals.":[74],"numerical":[76],"results,":[77],"showcased":[78],"paper,":[81],"serve":[82],"as":[83],"compelling":[85],"validation":[86],"notable":[89],"advantages":[90],"offered":[91],"our":[93],"innovative":[94],"approach.":[95],"Furthermore,":[96],"delves":[99],"into":[100],"impact":[102],"selecting":[104],"different":[105],"values,":[107],"contributing":[108,142],"deeper":[111],"understanding":[112],"algorithm\u2019s":[115],"behavior":[116],"across":[117],"spectrum":[119],"scenarios.":[121],"In":[122],"summary,":[123],"research":[125],"seeks":[126],"provide":[128],"practical":[130],"effective":[132],"solution":[133],"challenges":[136],"literature.":[147]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}