{"id":"https://openalex.org/W3119988406","doi":"https://doi.org/10.1080/00207160.2021.1875131","title":"A modified numerical algorithm based on fractional Euler functions for solving time-fractional partial differential equations","display_name":"A modified numerical algorithm based on fractional Euler functions for solving time-fractional partial differential equations","publication_year":2021,"publication_date":"2021-01-14","ids":{"openalex":"https://openalex.org/W3119988406","doi":"https://doi.org/10.1080/00207160.2021.1875131","mag":"3119988406"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2021.1875131","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1875131","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5081221970","display_name":"Haniye Dehestani","orcid":"https://orcid.org/0000-0001-6648-5547"},"institutions":[{"id":"https://openalex.org/I67080706","display_name":"Alzahra University","ror":"https://ror.org/013cdqc34","country_code":"IR","type":"education","lineage":["https://openalex.org/I67080706"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Haniye Dehestani","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran","institution_ids":["https://openalex.org/I67080706"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038764373","display_name":"Yadollah Ordokhani","orcid":"https://orcid.org/0000-0002-5167-6874"},"institutions":[{"id":"https://openalex.org/I67080706","display_name":"Alzahra University","ror":"https://ror.org/013cdqc34","country_code":"IR","type":"education","lineage":["https://openalex.org/I67080706"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Yadollah Ordokhani","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran","institution_ids":["https://openalex.org/I67080706"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038764373"],"corresponding_institution_ids":["https://openalex.org/I67080706"],"apc_list":null,"apc_paid":null,"fwci":0.42,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.54697443,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"98","issue":"10","first_page":"2078","last_page":"2096"},"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":0.9983999729156494,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9955000281333923,"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/mathematics","display_name":"Mathematics","score":0.7812492847442627},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6807523965835571},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6322140693664551},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5274959802627563},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5261406898498535},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45577266812324524},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44927796721458435},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.43991607427597046},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.42708495259284973},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4112653434276581},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35816603899002075},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3149893283843994},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1509724259376526},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.13457903265953064},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.09985965490341187}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7812492847442627},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6807523965835571},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6322140693664551},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5274959802627563},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5261406898498535},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45577266812324524},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44927796721458435},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.43991607427597046},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.42708495259284973},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4112653434276581},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35816603899002075},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3149893283843994},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1509724259376526},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.13457903265953064},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.09985965490341187},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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:10.1080/00207160.2021.1875131","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1875131","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W330595949","https://openalex.org/W912616841","https://openalex.org/W1983323635","https://openalex.org/W1990939959","https://openalex.org/W2000924596","https://openalex.org/W2020366383","https://openalex.org/W2020559479","https://openalex.org/W2042250814","https://openalex.org/W2042923669","https://openalex.org/W2045231411","https://openalex.org/W2057414857","https://openalex.org/W2071033102","https://openalex.org/W2209642378","https://openalex.org/W2271134218","https://openalex.org/W2500011369","https://openalex.org/W2562724410","https://openalex.org/W2779765306","https://openalex.org/W2791588350","https://openalex.org/W2804199579","https://openalex.org/W2947914989","https://openalex.org/W2970584391","https://openalex.org/W2983383822","https://openalex.org/W2998443321","https://openalex.org/W3011010596","https://openalex.org/W3029239832","https://openalex.org/W4211052487","https://openalex.org/W4238663582","https://openalex.org/W4242473853","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W2168857596","https://openalex.org/W322101810","https://openalex.org/W2384941625","https://openalex.org/W2131278000","https://openalex.org/W2009058751","https://openalex.org/W2478942264","https://openalex.org/W1989122168"],"abstract_inverted_index":{"A":[0],"novel":[1],"and":[2,105],"efficient":[3],"method":[4,15,46,64,110],"based":[5],"on":[6,31],"the":[7,13,26,45,49,59,62,66,93,103,108],"fractional":[8,28,38],"Euler":[9],"function":[10],"together":[11],"with":[12,58,113],"collocation":[14,63],"is":[16,96],"proposed":[17,109],"to":[18,37,68,101],"solve":[19],"time-fractional":[20],"partial":[21,39],"differential":[22],"equations.":[23,41],"By":[24],"applying":[25],"Riemann-Liouville":[27],"integral":[29],"operator":[30],"this":[32,90],"problem,":[33],"we":[34,43,85],"convert":[35],"it":[36],"integro-differential":[40],"Also,":[42],"present":[44],"of":[47,61,71,107],"calculating":[48],"operational":[50],"matrix":[51],"in":[52,111],"a":[53,69],"new":[54],"way.":[55],"These":[56],"matrices":[57],"help":[60],"reduce":[65],"problem":[67],"system":[70],"algebraic":[72],"equations":[73],"that":[74],"can":[75],"be":[76],"easily":[77],"solved":[78],"by":[79],"any":[80],"usual":[81],"numerical":[82,94],"methods.":[83,116],"Furthermore,":[84],"discuss":[86],"error":[87],"analysis":[88],"for":[89,98],"method.":[91],"Finally,":[92],"technique":[95],"implemented":[97],"several":[99],"examples":[100],"illustrate":[102],"superiority":[104],"efficiency":[106],"comparison":[112],"some":[114],"other":[115]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}