{"id":"https://openalex.org/W4406968373","doi":"https://doi.org/10.1007/s40314-025-03110-4","title":"A fractional hybrid function composed of block-pulses and fractional Fibonacci polynomials for solving multiterm fractional variable-order differential equations","display_name":"A fractional hybrid function composed of block-pulses and fractional Fibonacci polynomials for solving multiterm fractional variable-order differential equations","publication_year":2025,"publication_date":"2025-01-30","ids":{"openalex":"https://openalex.org/W4406968373","doi":"https://doi.org/10.1007/s40314-025-03110-4"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-025-03110-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03110-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03110-4.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03110-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075205392","display_name":"Octavian Postavaru","orcid":"https://orcid.org/0000-0003-2318-9742"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Octavian Postavaru","raw_affiliation_strings":["Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004126027","display_name":"Antonela Toma","orcid":"https://orcid.org/0000-0001-5472-394X"},"institutions":[{"id":"https://openalex.org/I61641377","display_name":"Universitatea Na\u021bional\u0103 de \u0218tiin\u021b\u0103 \u0219i Tehnologie Politehnica Bucure\u0219ti","ror":"https://ror.org/0558j5q12","country_code":"RO","type":"education","lineage":["https://openalex.org/I61641377"]}],"countries":["RO"],"is_corresponding":false,"raw_author_name":"Antonela Toma","raw_affiliation_strings":["Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Center for Research and Training in Innovative Techniques of Applied Mathematics in Engineering, University Politehnica of Bucharest, Splaiul Independentei 313, 060042, Bucharest, Romania","institution_ids":["https://openalex.org/I61641377"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075205392"],"corresponding_institution_ids":["https://openalex.org/I61641377"],"apc_list":null,"apc_paid":null,"fwci":1.4943,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.75411061,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"44","issue":"3","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":0.9998000264167786,"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":0.9998000264167786,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9979000091552734,"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"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9864000082015991,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.7125067710876465},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6817939877510071},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6684576272964478},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5727575421333313},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5543088316917419},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5140994191169739},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5067916512489319},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4941385090351105},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4898783564567566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4254935681819916},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3768318295478821},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36684757471084595},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2267015278339386},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2213725745677948},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.06476694345474243}],"concepts":[{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7125067710876465},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6817939877510071},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6684576272964478},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5727575421333313},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5543088316917419},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5140994191169739},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5067916512489319},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4941385090351105},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4898783564567566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4254935681819916},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3768318295478821},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36684757471084595},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2267015278339386},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2213725745677948},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.06476694345474243},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-025-03110-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03110-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03110-4.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s40314-025-03110-4","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s40314-025-03110-4","pdf_url":"https://link.springer.com/content/pdf/10.1007/s40314-025-03110-4.pdf","source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4406968373.pdf","grobid_xml":"https://content.openalex.org/works/W4406968373.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W839050305","https://openalex.org/W1571391776","https://openalex.org/W1965349501","https://openalex.org/W1966844238","https://openalex.org/W2017663693","https://openalex.org/W2041081306","https://openalex.org/W2066105773","https://openalex.org/W2076575482","https://openalex.org/W2082944446","https://openalex.org/W2412589306","https://openalex.org/W2755846920","https://openalex.org/W2798413892","https://openalex.org/W2938011410","https://openalex.org/W3086691244","https://openalex.org/W3182462261","https://openalex.org/W3193446317","https://openalex.org/W3212295336","https://openalex.org/W4200583955","https://openalex.org/W4244554442","https://openalex.org/W4280492599","https://openalex.org/W4289798260","https://openalex.org/W4295717590","https://openalex.org/W4300223101","https://openalex.org/W4384937438","https://openalex.org/W4390572150","https://openalex.org/W4391957401","https://openalex.org/W4391967790","https://openalex.org/W4396952351","https://openalex.org/W4403094948"],"related_works":["https://openalex.org/W2795454383","https://openalex.org/W2551890212","https://openalex.org/W2557230772","https://openalex.org/W4393146098","https://openalex.org/W2920386017","https://openalex.org/W4302325333","https://openalex.org/W4317662907","https://openalex.org/W4316467349","https://openalex.org/W2896847511","https://openalex.org/W2054041134"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"presents":[3],"the":[4,20,54,63,70,77,85,91,97,131,136],"development":[5],"of":[6,12,23,76,84,102,135],"a":[7,57],"fractional":[8,26,60,67,87],"hybrid":[9],"function":[10],"composed":[11],"block-pulse":[13],"functions":[14],"and":[15,47,66,133],"Fibonacci":[16],"polynomials":[17],"(FHBPF)":[18],"for":[19,142],"numerical":[21,125],"solution":[22],"multiterm":[24],"variable-order":[25],"differential":[27,98],"equations.":[28],"By":[29],"replacing":[30],"$$x\\rightarrow":[31],"x^{\\alpha":[32],"}$$":[33],"<mml:math":[34],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[35],"<mml:mrow>":[36],"<mml:mi>x</mml:mi>":[37,40],"<mml:mo>\u2192</mml:mo>":[38],"<mml:msup>":[39],"<mml:mi>\u03b1</mml:mi>":[41],"</mml:msup>":[42],"</mml:mrow>":[43],"</mml:math>":[44],"in":[45,62,69],"FHBPF":[46],"utilizing":[48],"incomplete":[49],"beta":[50],"functions,":[51],"we":[52,95],"construct":[53],"method":[55,79,120],"with":[56,109],"focus":[58],"on":[59],"derivatives":[61],"Caputo":[64],"sense":[65],"integrals":[68],"Riemann\u2013Liouville":[71,86],"sense.":[72],"A":[73],"key":[74],"advantage":[75],"proposed":[78],"is":[80,121],"its":[81,139],"exact":[82],"computation":[83],"integral":[88],"operator.":[89],"Using":[90],"Newton\u2013Cotes":[92],"collocation":[93],"method,":[94],"transform":[96],"equations":[99],"into":[100],"systems":[101],"algebraic":[103],"equations,":[104],"which":[105],"are":[106,127],"then":[107],"solved":[108],"traditional":[110],"techniques":[111],"such":[112],"as":[113],"Newton\u2019s":[114],"iterative":[115],"method.":[116],"An":[117],"error":[118],"analysis":[119],"also":[122],"introduced.":[123],"Several":[124],"examples":[126],"provided":[128],"to":[129],"demonstrate":[130],"effectiveness":[132],"simplicity":[134],"approach,":[137],"highlighting":[138],"efficiency":[140],"even":[141],"relatively":[143],"small":[144],"base":[145],"sizes.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-09T07:00:12.390032","created_date":"2025-10-10T00:00:00"}
