{"id":"https://openalex.org/W3005918476","doi":"https://doi.org/10.1142/s1793962320500154","title":"A superlinear numerical scheme for multi-term fractional nonlinear ordinary differential equations","display_name":"A superlinear numerical scheme for multi-term fractional nonlinear ordinary differential equations","publication_year":2020,"publication_date":"2020-02-13","ids":{"openalex":"https://openalex.org/W3005918476","doi":"https://doi.org/10.1142/s1793962320500154","mag":"3005918476"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962320500154","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320500154","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","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/A5081620783","display_name":"Jingna Zhang","orcid":"https://orcid.org/0009-0004-6575-6068"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingna Zhang","raw_affiliation_strings":["College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023621073","display_name":"Haobo Gong","orcid":null},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haobo Gong","raw_affiliation_strings":["College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089893371","display_name":"Sadia Arshad","orcid":"https://orcid.org/0000-0001-9085-5915"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Sadia Arshad","raw_affiliation_strings":["COMSATS University Islamabad, Lahore Campus, Pakistan"],"affiliations":[{"raw_affiliation_string":"COMSATS University Islamabad, Lahore Campus, Pakistan","institution_ids":["https://openalex.org/I16076960"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5022077594","display_name":"Jianfei Huang","orcid":"https://orcid.org/0000-0002-3793-1277"},"institutions":[{"id":"https://openalex.org/I78978612","display_name":"Yangzhou University","ror":"https://ror.org/03tqb8s11","country_code":"CN","type":"education","lineage":["https://openalex.org/I78978612"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianfei Huang","raw_affiliation_strings":["College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China","institution_ids":["https://openalex.org/I78978612"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081620783"],"corresponding_institution_ids":["https://openalex.org/I78978612"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00761976,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"11","issue":"02","first_page":"2050015","last_page":"2050015"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9990000128746033,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.820502758026123},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.6970505714416504},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6845705509185791},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6440790891647339},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6172515153884888},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5724209547042847},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5405288338661194},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5049040913581848},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5023229122161865},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4845484793186188},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.4792068898677826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4778580069541931},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.31581389904022217},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.060606449842453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.820502758026123},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.6970505714416504},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6845705509185791},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6440790891647339},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6172515153884888},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5724209547042847},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5405288338661194},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5049040913581848},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5023229122161865},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4845484793186188},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4792068898677826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4778580069541931},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.31581389904022217},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.060606449842453},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793962320500154","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320500154","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3024860944","display_name":null,"funder_award_id":"11871065","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W902939226","https://openalex.org/W1892527536","https://openalex.org/W1963675052","https://openalex.org/W1963902701","https://openalex.org/W1969312973","https://openalex.org/W1969547415","https://openalex.org/W1970213140","https://openalex.org/W1988571032","https://openalex.org/W1991982189","https://openalex.org/W2000434452","https://openalex.org/W2004373523","https://openalex.org/W2034401440","https://openalex.org/W2043665547","https://openalex.org/W2068263981","https://openalex.org/W2084562241","https://openalex.org/W2091946269","https://openalex.org/W2111271983","https://openalex.org/W2116896358","https://openalex.org/W2130538136","https://openalex.org/W2139227432","https://openalex.org/W2227709011","https://openalex.org/W2745111427","https://openalex.org/W2754735025","https://openalex.org/W2767759558","https://openalex.org/W2803663761","https://openalex.org/W2803893437","https://openalex.org/W2893600178","https://openalex.org/W2963309992","https://openalex.org/W4244854774","https://openalex.org/W4247953052","https://openalex.org/W4303005599"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2253351617","https://openalex.org/W1975289146","https://openalex.org/W4246784705","https://openalex.org/W3121927021","https://openalex.org/W2105887828","https://openalex.org/W4390948881","https://openalex.org/W2122599759","https://openalex.org/W2043671984"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"present":[4],"a":[5],"superlinear":[6],"numerical":[7,88],"method":[8],"for":[9],"multi-term":[10,29],"fractional":[11,43,79],"nonlinear":[12],"ordinary":[13],"differential":[14],"equations":[15],"(MTFNODEs).":[16],"First,":[17],"the":[18,33,42,46,52,58,73,76,82,94],"presented":[19],"problem":[20],"is":[21,38],"equivalently":[22],"transformed":[23],"into":[24],"its":[25],"integral":[26],"form":[27],"with":[28,51],"Riemann\u2013Liouville":[30],"integrals.":[31,44],"Second,":[32],"compound":[34],"product":[35],"trapezoidal":[36],"rule":[37],"used":[39],"to":[40,92],"approximate":[41],"Then,":[45],"unconditional":[47],"stability":[48],"and":[49,68,75],"convergence":[50],"order":[53],"[Formula:":[54,65,69],"see":[55,66,70],"text]":[56,67,71],"of":[57],"proposed":[59],"scheme":[60],"are":[61,72,90],"strictly":[62],"established,":[63],"where":[64],"maximum":[74,78],"second":[77],"indexes":[80],"in":[81],"considered":[83],"MTFNODEs,":[84],"respectively.":[85],"Finally,":[86],"two":[87],"examples":[89],"provided":[91],"support":[93],"theoretical":[95],"results.":[96]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}