{"id":"https://openalex.org/W2036409092","doi":"https://doi.org/10.1142/s021812741250071x","title":"GENERALIZED FRACTIONAL ORDER BLOCH EQUATION WITH EXTENDED DELAY","display_name":"GENERALIZED FRACTIONAL ORDER BLOCH EQUATION WITH EXTENDED DELAY","publication_year":2012,"publication_date":"2012-03-14","ids":{"openalex":"https://openalex.org/W2036409092","doi":"https://doi.org/10.1142/s021812741250071x","mag":"2036409092"},"language":"en","primary_location":{"id":"doi:10.1142/s021812741250071x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250071x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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 Bifurcation and Chaos","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/A5060837002","display_name":"Sachin Bhalekar","orcid":"https://orcid.org/0000-0003-1981-8171"},"institutions":[{"id":"https://openalex.org/I141641110","display_name":"Shivaji University","ror":"https://ror.org/01bsn4x02","country_code":"IN","type":"education","lineage":["https://openalex.org/I141641110"]},{"id":"https://openalex.org/I878213199","display_name":"Savitribai Phule Pune University","ror":"https://ror.org/044g6d731","country_code":"IN","type":"education","lineage":["https://openalex.org/I878213199"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"SACHIN BHALEKAR","raw_affiliation_strings":["Department of Mathematics, Shivaji University, Kolhapur 416004, India","Department of Mathematics, University of Pune, Pune 411007, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shivaji University, Kolhapur 416004, India","institution_ids":["https://openalex.org/I141641110"]},{"raw_affiliation_string":"Department of Mathematics, University of Pune, Pune 411007, India","institution_ids":["https://openalex.org/I878213199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025802059","display_name":"Varsha Daftardar\u2010Gejji","orcid":"https://orcid.org/0000-0002-0277-462X"},"institutions":[{"id":"https://openalex.org/I878213199","display_name":"Savitribai Phule Pune University","ror":"https://ror.org/044g6d731","country_code":"IN","type":"education","lineage":["https://openalex.org/I878213199"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"VARSHA DAFTARDAR-GEJJI","raw_affiliation_strings":["Department of Mathematics, University of Pune, Pune 411007, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Pune, Pune 411007, India","institution_ids":["https://openalex.org/I878213199"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030756029","display_name":"Dumitru B\u01celeanu","orcid":"https://orcid.org/0000-0002-0286-7244"},"institutions":[{"id":"https://openalex.org/I106245021","display_name":"\u00c7ankaya University","ror":"https://ror.org/056wqre19","country_code":"TR","type":"education","lineage":["https://openalex.org/I106245021"]},{"id":"https://openalex.org/I4210142834","display_name":"Institute of Space Science - INFLPR Subsidiary","ror":"https://ror.org/054a6wv56","country_code":"RO","type":"facility","lineage":["https://openalex.org/I4210142834"]}],"countries":["RO","TR"],"is_corresponding":false,"raw_author_name":"DUMITRU BALEANU","raw_affiliation_strings":["Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey","Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey","institution_ids":["https://openalex.org/I106245021"]},{"raw_affiliation_string":"Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania","institution_ids":["https://openalex.org/I4210142834"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006675553","display_name":"Richard L. Magin","orcid":"https://orcid.org/0000-0002-5103-1611"},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]},{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"RICHARD MAGIN","raw_affiliation_strings":["Department of Bioengineering, University of Illinois, 851 S. Morgan St., Chicago 60607, USA","Department of Bioengineering, University of Illinois, 851 S. Morgan St., Chicago, 60607, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Bioengineering, University of Illinois, 851 S. Morgan St., Chicago 60607, USA","institution_ids":["https://openalex.org/I39422238"]},{"raw_affiliation_string":"Department of Bioengineering, University of Illinois, 851 S. Morgan St., Chicago, 60607, USA#TAB#","institution_ids":["https://openalex.org/I157725225","https://openalex.org/I39422238"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5060837002"],"corresponding_institution_ids":["https://openalex.org/I141641110","https://openalex.org/I878213199"],"apc_list":null,"apc_paid":null,"fwci":5.27090467,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.96215596,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"22","issue":"04","first_page":"1250071","last_page":"1250071"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9991000294685364,"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":0.9991000294685364,"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/T12603","display_name":"NMR spectroscopy and applications","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy 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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.9589999914169312,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bloch-equations","display_name":"Bloch equations","score":0.8047267198562622},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7276737093925476},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6793606877326965},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.487439900636673},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.47289004921913147},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45786479115486145},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.414575457572937},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.30634284019470215}],"concepts":[{"id":"https://openalex.org/C142951617","wikidata":"https://www.wikidata.org/wiki/Q651707","display_name":"Bloch equations","level":2,"score":0.8047267198562622},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7276737093925476},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6793606877326965},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.487439900636673},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47289004921913147},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45786479115486145},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.414575457572937},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.30634284019470215},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021812741250071x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021812741250071x","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"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 Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W110285710","https://openalex.org/W193812311","https://openalex.org/W194858719","https://openalex.org/W433794350","https://openalex.org/W617206983","https://openalex.org/W1502089761","https://openalex.org/W1521875821","https://openalex.org/W1530054495","https://openalex.org/W1589163079","https://openalex.org/W1854566075","https://openalex.org/W1979006914","https://openalex.org/W1991212918","https://openalex.org/W1992769555","https://openalex.org/W1998561306","https://openalex.org/W2001509015","https://openalex.org/W2008107284","https://openalex.org/W2019231090","https://openalex.org/W2021987648","https://openalex.org/W2027497334","https://openalex.org/W2029942023","https://openalex.org/W2045256358","https://openalex.org/W2051182120","https://openalex.org/W2055181214","https://openalex.org/W2059291376","https://openalex.org/W2068760248","https://openalex.org/W2082025849","https://openalex.org/W2085136674","https://openalex.org/W2092158279","https://openalex.org/W2092979307","https://openalex.org/W2120862100","https://openalex.org/W2134947167","https://openalex.org/W2299647821","https://openalex.org/W2483375472","https://openalex.org/W2787959293","https://openalex.org/W3004024615","https://openalex.org/W3169436701","https://openalex.org/W4236369371","https://openalex.org/W4239838448","https://openalex.org/W4251462398","https://openalex.org/W4253062931","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2642160037","https://openalex.org/W1985995605","https://openalex.org/W2082446734","https://openalex.org/W2052845109","https://openalex.org/W2055557864","https://openalex.org/W4313560640","https://openalex.org/W1970979661","https://openalex.org/W4246784705","https://openalex.org/W2253351617","https://openalex.org/W2164861497"],"abstract_inverted_index":{"The":[0,55,86,102],"fundamental":[1],"description":[2],"of":[3,30,52,69,80,111],"relaxation":[4,123],"(T":[5],"1":[6,97,104],"and":[7,34,98,153,158,189],"T":[8,96,99,103,121],"2":[9,100,122],")":[10],"in":[11,60,91,124,146,148,154],"nuclear":[12],"magnetic":[13],"resonance":[14,188],"(NMR)":[15],"is":[16,106,142],"provided":[17],"by":[18,162],"the":[19,61,73,77,92,109,120,140,150,155,168,173],"Bloch":[20,45,62,174],"equation,":[21,175],"an":[22,49,83],"integer-order":[23],"ordinary":[24],"differential":[25],"equation":[26,46,63],"that":[27,47,178],"interrelates":[28],"precession":[29],"magnetization":[31,81],"with":[32,82],"time-":[33],"space-dependent":[35],"relaxation.":[36,101,190],"In":[37],"this":[38,125],"paper,":[39],"we":[40,176,179],"propose":[41],"a":[42,64,129,182],"fractional":[43,56,169],"order":[44],"includes":[48],"extended":[50,126,164],"model":[51,127,152,171,185],"time":[53,57,74,165],"delays.":[54],"derivative":[58,170],"embeds":[59],"fading":[65],"power":[66],"law":[67],"form":[68],"system":[70,141,151],"memory":[71],"while":[72,119],"delay":[75,131,166],"averages":[76],"present":[78],"value":[79],"earlier":[84],"one.":[85],"analysis":[87],"shows":[88],"different":[89],"patterns":[90],"stability":[93],"behavior":[94],"for":[95,108,172,186],"decay":[105],"stable":[107],"range":[110],"delays":[112],"tested":[113],"(1":[114],"\u03bcsec":[115,134],"to":[116,135,167],"200":[117,136],"\u03bcsec),":[118],"exhibits":[128],"critical":[130],"(typically":[132],"100":[133],"\u03bcsec)":[137],"above":[138],"which":[139],"unstable.":[143],"Delays":[144],"arise":[145],"NMR":[147,187],"both":[149],"signal":[156],"excitation":[157],"detection":[159],"processes.":[160],"Therefore,":[161],"adding":[163],"believe":[177],"can":[180],"develop":[181],"more":[183],"appropriate":[184]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":9},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}