{"id":"https://openalex.org/W2985382023","doi":"https://doi.org/10.1007/s40314-019-0936-z","title":"A cardinal method to solve coupled nonlinear variable-order time fractional sine-Gordon equations","display_name":"A cardinal method to solve coupled nonlinear variable-order time fractional sine-Gordon equations","publication_year":2019,"publication_date":"2019-10-22","ids":{"openalex":"https://openalex.org/W2985382023","doi":"https://doi.org/10.1007/s40314-019-0936-z","mag":"2985382023"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-019-0936-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-019-0936-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","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/A5074418418","display_name":"Mohammad Heydari","orcid":"https://orcid.org/0000-0001-6764-4394"},"institutions":[{"id":"https://openalex.org/I204490172","display_name":"Shiraz University of Technology","ror":"https://ror.org/04bxa3v83","country_code":"IR","type":"education","lineage":["https://openalex.org/I204490172"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Mohammad Hossein Heydari","raw_affiliation_strings":["Department of Mathematics, Shiraz University of Technology, Shiraz, Iran"],"raw_orcid":"https://orcid.org/0000-0001-6764-4394","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shiraz University of Technology, Shiraz, Iran","institution_ids":["https://openalex.org/I204490172"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015962889","display_name":"Z. Avazzadeh","orcid":"https://orcid.org/0000-0003-2257-1798"},"institutions":[{"id":"https://openalex.org/I69356397","display_name":"Xi\u2019an Jiaotong-Liverpool University","ror":"https://ror.org/03zmrmn05","country_code":"CN","type":"education","lineage":["https://openalex.org/I69356397"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zakieh Avazzadeh","raw_affiliation_strings":["Department of Mathematical Sciences, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123, Jiangsu, China","Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, Jiangsu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Xi\u2019an Jiaotong-Liverpool University, Suzhou, 215123, Jiangsu, China","institution_ids":["https://openalex.org/I69356397"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, 215123, Jiangsu, China","institution_ids":["https://openalex.org/I69356397"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024865406","display_name":"Yin Yang","orcid":"https://orcid.org/0000-0002-7435-152X"},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yin Yang","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing, Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Key Laboratory of Intelligent Computing, Information Processing of Ministry of Education, School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022405104","display_name":"Carlo Cattani","orcid":"https://orcid.org/0000-0002-7504-0424"},"institutions":[{"id":"https://openalex.org/I138938424","display_name":"Universit\u00e0 degli Studi della Tuscia","ror":"https://ror.org/03svwq685","country_code":"IT","type":"education","lineage":["https://openalex.org/I138938424"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Cattani","raw_affiliation_strings":["Engineering School (DEIM), University of Tuscia, Viterbo, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering School (DEIM), University of Tuscia, Viterbo, Italy","institution_ids":["https://openalex.org/I138938424"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5074418418"],"corresponding_institution_ids":["https://openalex.org/I204490172"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":1.8403,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.84929602,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":"39","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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":0.9980999827384949,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7192652225494385},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.7121782302856445},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.580536425113678},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5729314088821411},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5373934507369995},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5182480812072754},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.49179771542549133},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.48358219861984253},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4474779963493347},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43521901965141296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32796207070350647},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17279458045959473}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7192652225494385},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7121782302856445},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.580536425113678},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5729314088821411},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5373934507369995},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5182480812072754},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.49179771542549133},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.48358219861984253},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4474779963493347},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43521901965141296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32796207070350647},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17279458045959473},{"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},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-019-0936-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-019-0936-z","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W1805381866","https://openalex.org/W1969399740","https://openalex.org/W2011508769","https://openalex.org/W2016124038","https://openalex.org/W2041393921","https://openalex.org/W2050981193","https://openalex.org/W2070169038","https://openalex.org/W2073654789","https://openalex.org/W2074445296","https://openalex.org/W2141205646","https://openalex.org/W2158629510","https://openalex.org/W2342455717","https://openalex.org/W2408478130","https://openalex.org/W2494775221","https://openalex.org/W2522468891","https://openalex.org/W2562874578","https://openalex.org/W2567155074","https://openalex.org/W2567904062","https://openalex.org/W2601612027","https://openalex.org/W2604763123","https://openalex.org/W2604906738","https://openalex.org/W2604931151","https://openalex.org/W2622597077","https://openalex.org/W2769326112","https://openalex.org/W2770801977","https://openalex.org/W2772500265","https://openalex.org/W2787959293","https://openalex.org/W2789789392","https://openalex.org/W2789907329","https://openalex.org/W2792222068","https://openalex.org/W2803701812","https://openalex.org/W2804797285","https://openalex.org/W2888454544","https://openalex.org/W2893162802","https://openalex.org/W2894413670","https://openalex.org/W2896885197","https://openalex.org/W2902014757","https://openalex.org/W2913123966","https://openalex.org/W2914047918","https://openalex.org/W2918865039","https://openalex.org/W2922153620","https://openalex.org/W2925828089","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2886467464","https://openalex.org/W4246784705","https://openalex.org/W2352756630","https://openalex.org/W2253351617","https://openalex.org/W2358475213","https://openalex.org/W2065284654","https://openalex.org/W4390948881","https://openalex.org/W2588958454"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":6}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}