{"id":"https://openalex.org/W3048832441","doi":"https://doi.org/10.1142/s1793005721500034","title":"New Method for Numerical Solution of Z-Fractional Differential Equations","display_name":"New Method for Numerical Solution of Z-Fractional Differential Equations","publication_year":2020,"publication_date":"2020-08-12","ids":{"openalex":"https://openalex.org/W3048832441","doi":"https://doi.org/10.1142/s1793005721500034","mag":"3048832441"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005721500034","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005721500034","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"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":"New Mathematics and Natural Computation","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/A5004679523","display_name":"Parisa Keshavarz","orcid":null},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Parisa Keshavarz","raw_affiliation_strings":["Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran","institution_ids":["https://openalex.org/I4210089026"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073095019","display_name":"Tofigh Allahviranloo","orcid":"https://orcid.org/0000-0002-6673-3560"},"institutions":[{"id":"https://openalex.org/I128277893","display_name":"Bah\u00e7e\u015fehir University","ror":"https://ror.org/00yze4d93","country_code":"TR","type":"education","lineage":["https://openalex.org/I128277893"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Tofigh Allahviranloo","raw_affiliation_strings":["Faculty of Engineering and Natural Sciences, Bahcesehir University, \u00c7\u0131ra\u011fan Cd., Beshiktash, 34353 Istanbul, Turkey"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Natural Sciences, Bahcesehir University, \u00c7\u0131ra\u011fan Cd., Beshiktash, 34353 Istanbul, Turkey","institution_ids":["https://openalex.org/I128277893"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054668691","display_name":"Farajollah Mohammadi Yaghoobi","orcid":"https://orcid.org/0000-0002-0558-3327"},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Farajollah M. Yaghoobi","raw_affiliation_strings":["Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran","institution_ids":["https://openalex.org/I4210089026"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077459661","display_name":"Ali Barahmand","orcid":"https://orcid.org/0000-0001-9110-1971"},"institutions":[{"id":"https://openalex.org/I4210089026","display_name":"Islamic Azad University of Hamedan","ror":"https://ror.org/007zpd132","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I4210089026"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Ali Barahmand","raw_affiliation_strings":["Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hamedan Branch, Islamic Azad University, Prof. Mousivand Blvd, Imam Khomeini Blvd, Hamedan 6518115743, Iran","institution_ids":["https://openalex.org/I4210089026"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0339,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.36587064,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"17","issue":"01","first_page":"45","last_page":"61"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T12135","display_name":"Fuzzy Systems and Optimization","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9948999881744385,"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":0.8036323189735413},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6338297724723816},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5403324365615845},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49834275245666504},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.47362133860588074},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4165305495262146},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.4142382740974426},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3807764947414398}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8036323189735413},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6338297724723816},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5403324365615845},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49834275245666504},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.47362133860588074},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4165305495262146},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.4142382740974426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3807764947414398}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1142/s1793005721500034","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005721500034","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"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":"New Mathematics and Natural Computation","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:wsi:nmncxx:v:17:y:2021:i:01:n:s1793005721500034","is_oa":false,"landing_page_url":"http://www.worldscientific.com/doi/abs/10.1142/S1793005721500034","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1033706657","https://openalex.org/W1975670568","https://openalex.org/W1997952930","https://openalex.org/W2042774699","https://openalex.org/W2062690169","https://openalex.org/W2080917899","https://openalex.org/W2089572792","https://openalex.org/W2146226785","https://openalex.org/W2738730524","https://openalex.org/W2790388419","https://openalex.org/W2884661192","https://openalex.org/W2903958362","https://openalex.org/W4230835027","https://openalex.org/W4242361967","https://openalex.org/W4247219141","https://openalex.org/W4254628720"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W4246784705","https://openalex.org/W2253351617","https://openalex.org/W2065284654","https://openalex.org/W4390948881","https://openalex.org/W3121927021","https://openalex.org/W4312805195","https://openalex.org/W2111177161","https://openalex.org/W4205839918"],"abstract_inverted_index":{"In":[0],"this":[1,63],"paper,":[2],"at":[3],"first,":[4],"we":[5,15,132],"introduce":[6],"fractional":[7,35,46,90,142],"differential":[8,91,143],"equations":[9,144],"with":[10,86,145],"[Formula:":[11,75,83,146],"see":[12,76,84,147],"text]-valuation.":[13,148],"Then,":[14],"propose":[16],"a":[17,28],"numerical":[18],"method":[19,26,30,37,48,64,137],"to":[20,119],"approximate":[21,140],"the":[22,33,39,44,51,56,69,74,87,97,100,104,121,124,135,141],"solution.":[23],"The":[24,108],"proposed":[25,61,136],"is":[27,60,111],"hybrid":[29],"based":[31,49,112],"on":[32,50,96,113],"corrected":[34,45],"Euler\u2019s":[36,47],"and":[38,55,103,117],"probability":[40,109],"distribution":[41,115],"function.":[42],"Moreover,":[43],"generalized":[52,105],"Taylor":[53],"formula":[54],"modified":[57],"trapezoidal":[58],"rule":[59],"that":[62,134],"can":[65,138],"be":[66],"used":[67,118],"in":[68],"problems\u2019":[70],"limitation":[71,126],"section":[72],"of":[73,81,99,123],"text]-fractional":[77],"Initial":[78],"value":[79],"problem":[80,125],"order":[82],"text]":[85],"fuzzy":[88,106],"Caputo":[89],"(fractional":[92],"derivatives":[93],"are":[94],"defined":[95],"basis":[98],"Hukuhara":[101],"differences":[102],"derivatives).":[107],"function":[110,116],"exponential":[114],"represent":[120],"reliability":[122],"part.":[127],"Finally,":[128],"by":[129],"two":[130],"examples,":[131],"show":[133],"arbitrarily":[139]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
