{"id":"https://openalex.org/W4280576228","doi":"https://doi.org/10.1080/00207160.2022.2078663","title":"Fractional second linear multistep methods: the explicit forms for solving fractional differential equations and stability analysis","display_name":"Fractional second linear multistep methods: the explicit forms for solving fractional differential equations and stability analysis","publication_year":2022,"publication_date":"2022-05-14","ids":{"openalex":"https://openalex.org/W4280576228","doi":"https://doi.org/10.1080/00207160.2022.2078663"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2078663","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2078663","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer 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/A5028380039","display_name":"Safar Irandoust\u2010Pakchin","orcid":"https://orcid.org/0000-0001-9548-4762"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Safar Irandoust-Pakchin","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066812840","display_name":"Somayeh Abdi-Mazraeh","orcid":"https://orcid.org/0000-0003-3753-5474"},"institutions":[{"id":"https://openalex.org/I41832843","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I41832843"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Somayeh Abdi-Mazraeh","raw_affiliation_strings":["Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran","institution_ids":["https://openalex.org/I41832843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028380039"],"corresponding_institution_ids":["https://openalex.org/I41832843"],"apc_list":null,"apc_paid":null,"fwci":0.5411,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57824863,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"100","issue":"1","first_page":"20","last_page":"46"},"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":0.9980000257492065,"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/T11081","display_name":"Advanced Control Systems Design","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8924822807312012},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.7972346544265747},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6093723177909851},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6090548634529114},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.594221293926239},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5581503510475159},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5560664534568787},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.4868995249271393},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.45791497826576233},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4250534772872925},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.4111226499080658},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3768593966960907},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.23399019241333008},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.1432797908782959},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.07678663730621338}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8924822807312012},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.7972346544265747},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6093723177909851},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6090548634529114},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.594221293926239},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5581503510475159},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5560664534568787},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.4868995249271393},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.45791497826576233},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4250534772872925},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.4111226499080658},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3768593966960907},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.23399019241333008},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.1432797908782959},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.07678663730621338},{"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/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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2078663","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2078663","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1421227476","display_name":null,"funder_award_id":"3902","funder_id":"https://openalex.org/F4320324703","funder_display_name":"University of Tabriz"}],"funders":[{"id":"https://openalex.org/F4320324703","display_name":"University of Tabriz","ror":"https://ror.org/01papkj44"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W91283514","https://openalex.org/W212594717","https://openalex.org/W577449674","https://openalex.org/W902939226","https://openalex.org/W1436001274","https://openalex.org/W1584611818","https://openalex.org/W1963581131","https://openalex.org/W1985294906","https://openalex.org/W1990956480","https://openalex.org/W1991982189","https://openalex.org/W2000434452","https://openalex.org/W2003437637","https://openalex.org/W2005114389","https://openalex.org/W2054709933","https://openalex.org/W2068928911","https://openalex.org/W2083559699","https://openalex.org/W2091613684","https://openalex.org/W2152152827","https://openalex.org/W2313278888","https://openalex.org/W2509431182","https://openalex.org/W2787959293","https://openalex.org/W2989377415","https://openalex.org/W3000686282","https://openalex.org/W3006771970","https://openalex.org/W3105813679","https://openalex.org/W4253062931"],"related_works":["https://openalex.org/W2005214638","https://openalex.org/W1966814806","https://openalex.org/W2912618248","https://openalex.org/W3033917653","https://openalex.org/W2118026205","https://openalex.org/W2142355058","https://openalex.org/W2275160292","https://openalex.org/W4318309765","https://openalex.org/W3082972026","https://openalex.org/W4224117355"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,7,23,47,57,65,80,91,95,102,113],"explicit":[4,28,86],"forms":[5],"of":[6,22,54,59,67,75,82,84,94],"fractional":[8,18,34,68],"second":[9],"linear":[10,77],"multistep":[11],"methods":[12,87,97],"(FSLMMs)":[13],"are":[14,30,88,98,109],"introduced":[15],"for":[16],"solving":[17],"differential":[19],"equations":[20],"(FDEs)":[21],"fractional-order":[24],"in":[25,101],"(1,2).":[26,72],"These":[27],"FSLMMs":[29],"constructed":[31],"based":[32],"on":[33],"backward":[35],"difference":[36],"formulas":[37],"1,":[38],"2,":[39],"and":[40,44,51,79],"3":[41],"(FBDF1,":[42],"FBDF2,":[43],"FBDF3)":[45],"with":[46],"first,":[48],"second,":[49],"third,":[50],"fourth":[52],"orders":[53],"convergence.":[55],"Also,":[56],"monotonicity":[58],"these":[60,85],"FBDFs":[61],"is":[62],"considered":[63],"when":[64],"order":[66,74,81],"derivatives":[69],"lies":[70],"into":[71],"The":[73],"consistency,":[76],"stability,":[78],"convergence":[83],"analysed.":[89],"Moreover,":[90],"stability":[92,103],"regions":[93],"proposed":[96,114],"completely":[99],"studied":[100],"topic.":[104],"Finally,":[105],"four":[106],"experimental":[107],"examples":[108],"presented":[110],"to":[111],"confirm":[112],"theories.":[115]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}