{"id":"https://openalex.org/W2923916604","doi":"https://doi.org/10.1007/s00366-019-00736-x","title":"Numerical approach for solving variable-order space\u2013time fractional telegraph equation using transcendental Bernstein series","display_name":"Numerical approach for solving variable-order space\u2013time fractional telegraph equation using transcendental Bernstein series","publication_year":2019,"publication_date":"2019-03-27","ids":{"openalex":"https://openalex.org/W2923916604","doi":"https://doi.org/10.1007/s00366-019-00736-x","mag":"2923916604"},"language":"en","primary_location":{"id":"doi:10.1007/s00366-019-00736-x","doi":"https://doi.org/10.1007/s00366-019-00736-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-019-00736-x","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040688350","display_name":"Hossein Hassani","orcid":"https://orcid.org/0000-0001-6916-1492","observed_orcids":["https://orcid.org/0000-0001-6916-1492"]},"institutions":[{"id":"https://openalex.org/I127908078","display_name":"Shahrekord University","ror":"https://ror.org/051rngw70","country_code":"IR","type":"education","lineage":["https://openalex.org/I127908078"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"H. Hassani","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Iran","institution_ids":["https://openalex.org/I127908078"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015962889","display_name":"Zakieh Avazzadeh","orcid":"https://orcid.org/0000-0003-2257-1798","observed_orcids":["https://orcid.org/0000-0003-2257-1798"]},"institutions":[{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. Avazzadeh","raw_affiliation_strings":["School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5035539918","display_name":"J. A. Tenreiro Machado","orcid":"https://orcid.org/0000-0003-4274-4879","observed_orcids":["https://orcid.org/0000-0003-4274-4879"]},"institutions":[{"id":"https://openalex.org/I83863532","display_name":"Universidade T\u00e9cnica do Porto","ror":"https://ror.org/04988re48","country_code":"PT","type":"education","lineage":["https://openalex.org/I83863532"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"J. A. Tenreiro Machado","raw_affiliation_strings":["Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. Ant\u00f3nio Bernardino de Almeida, 4249-015, Porto 431, Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, R. Dr. Ant\u00f3nio Bernardino de Almeida, 4249-015, Porto 431, Portugal","institution_ids":["https://openalex.org/I83863532"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5040688350"],"corresponding_institution_ids":["https://openalex.org/I127908078"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":4.4142,"has_fulltext":false,"cited_by_count":73,"citation_normalized_percentile":{"value":0.95236181,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"36","issue":"3","first_page":"867","last_page":"878"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9955999851226807,"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":0.9955999851226807,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.0007999999797903001,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/variable-order-fractional-derivative","display_name":"variable-order fractional derivative","score":0.8330000042915344},{"id":"https://openalex.org/keywords/caputo-fractional-derivative","display_name":"Caputo fractional derivative","score":0.8740000128746033},{"id":"https://openalex.org/keywords/operational-matrix","display_name":"operational matrices","score":0.9079999923706055},{"id":"https://openalex.org/keywords/lagrange-multiplier-method","display_name":"Lagrange multipliers","score":0.7889999747276306},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7120000123977661},{"id":"https://openalex.org/keywords/numerical-solution-of-fractional-differential-equations","display_name":"numerical solution of fractional differential equations","score":0.7379999756813049}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.757835865020752},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6352403163909912},{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.6054797172546387},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.602078914642334},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5829116702079773},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5813701748847961},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.5494953989982605},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.506897509098053},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.47064536809921265},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4547031819820404},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.41216713190078735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37294113636016846},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.24823403358459473},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00366-019-00736-x","doi":"https://doi.org/10.1007/s00366-019-00736-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00366-019-00736-x","pdf_url":null,"source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-70","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Engineering with Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1509146820","https://openalex.org/W1965027360","https://openalex.org/W1970741096","https://openalex.org/W1983159263","https://openalex.org/W1994128207","https://openalex.org/W1994916853","https://openalex.org/W1999341439","https://openalex.org/W2001514844","https://openalex.org/W2002415091","https://openalex.org/W2005114389","https://openalex.org/W2007866354","https://openalex.org/W2010016067","https://openalex.org/W2013243433","https://openalex.org/W2024093795","https://openalex.org/W2047623457","https://openalex.org/W2054899953","https://openalex.org/W2058330335","https://openalex.org/W2060303523","https://openalex.org/W2062163287","https://openalex.org/W2063133641","https://openalex.org/W2064085340","https://openalex.org/W2065685184","https://openalex.org/W2073180729","https://openalex.org/W2103233901","https://openalex.org/W2103725449","https://openalex.org/W2107221565","https://openalex.org/W2185695324","https://openalex.org/W2232246260","https://openalex.org/W2277623713","https://openalex.org/W2282745915","https://openalex.org/W2324311522","https://openalex.org/W2343525598","https://openalex.org/W2562874578","https://openalex.org/W2567155074","https://openalex.org/W2567904062","https://openalex.org/W2606432427","https://openalex.org/W2724838443","https://openalex.org/W2731185405","https://openalex.org/W2756329465","https://openalex.org/W2774844421","https://openalex.org/W3020099039"],"related_works":["https://openalex.org/W2564305598","https://openalex.org/W2919348289","https://openalex.org/W3015564060","https://openalex.org/W2960977029","https://openalex.org/W2937708686","https://openalex.org/W2958014349","https://openalex.org/W2910387264","https://openalex.org/W2923702436","https://openalex.org/W2522158891","https://openalex.org/W2276951432"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":16},{"year":2019,"cited_by_count":5}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2019-04-01T00:00:00"}