{"id":"https://openalex.org/W7208720927","doi":"https://doi.org/10.1002/jnm.70200","title":"A Numerical Method for Solving Systems of Fractional Stochastic Delay Differential Equations","display_name":"A Numerical Method for Solving Systems of Fractional Stochastic Delay Differential Equations","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7208720927","doi":"https://doi.org/10.1002/jnm.70200"},"language":"en","primary_location":{"id":"doi:10.1002/jnm.70200","doi":"https://doi.org/10.1002/jnm.70200","is_oa":true,"landing_page_url":"https://doi.org/10.1002/jnm.70200","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/jnm.70200","source":{"id":"https://openalex.org/S201890602","display_name":"International Journal of Numerical Modelling Electronic Networks Devices and Fields","issn_l":"0894-3370","issn":["0894-3370","1099-1204"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Numerical Modelling: Electronic Networks, Devices and Fields","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/jnm.70200","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5150018740","display_name":"Fateme Yari","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210146087","display_name":"Malayer University","ror":"https://ror.org/03rk9sq81","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210146087"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Fateme Yari","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran","institution_ids":["https://openalex.org/I4210146087"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074918653","display_name":"Farshid Mirzaee","orcid":"https://orcid.org/0000-0002-1429-2548","observed_orcids":["https://orcid.org/0000-0002-1429-2548"]},"institutions":[{"id":"https://openalex.org/I4210146087","display_name":"Malayer University","ror":"https://ror.org/03rk9sq81","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210146087"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Farshid Mirzaee","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran"],"raw_orcid":"https://orcid.org/0000-0002-1429-2548","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran","institution_ids":["https://openalex.org/I4210146087"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081617291","display_name":"Erfan Solhi","orcid":"https://orcid.org/0000-0001-6950-8177","observed_orcids":["https://orcid.org/0000-0001-6950-8177"]},"institutions":[{"id":"https://openalex.org/I4210146087","display_name":"Malayer University","ror":"https://ror.org/03rk9sq81","country_code":"IR","type":"education","lineage":["https://openalex.org/I4210146087"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Erfan Solhi","raw_affiliation_strings":["Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran"],"raw_orcid":"https://orcid.org/0000-0001-6950-8177","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Mathematical Sciences and Statistics Malayer University  Malayer Iran","institution_ids":["https://openalex.org/I4210146087"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5074918653"],"corresponding_institution_ids":["https://openalex.org/I4210146087"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"39","issue":"5","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.6723999977111816,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.6723999977111816,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.2897999882698059,"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":0.020500000566244125,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/block-pulse-functions","display_name":"block-pulse functions","score":0.9769999980926514},{"id":"https://openalex.org/keywords/collocation-method","display_name":"collocation method","score":0.8479999899864197},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7070000171661377},{"id":"https://openalex.org/keywords/error-bounds","display_name":"error bounds","score":0.9739999771118164},{"id":"https://openalex.org/keywords/memory-effects","display_name":"memory effects","score":0.5640000104904175},{"id":"https://openalex.org/keywords/time-delay","display_name":"time delay","score":0.6809999942779541}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6128000020980835},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5209000110626221},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.4961000084877014},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.492000013589859},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4851999878883362},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4726000130176544},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4009999930858612},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3873000144958496},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.37689998745918274},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.3756999969482422},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.37220001220703125},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36959999799728394},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.3628999888896942},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3456000089645386},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.3156000077724457},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.31380000710487366},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3124000132083893},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3061999976634979},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.3061000108718872},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.2879999876022339},{"id":"https://openalex.org/C5806529","wikidata":"https://www.wikidata.org/wiki/Q2365325","display_name":"Orthonormal basis","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.2556000053882599},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.2515000104904175}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jnm.70200","doi":"https://doi.org/10.1002/jnm.70200","is_oa":true,"landing_page_url":"https://doi.org/10.1002/jnm.70200","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/jnm.70200","source":{"id":"https://openalex.org/S201890602","display_name":"International Journal of Numerical Modelling Electronic Networks Devices and Fields","issn_l":"0894-3370","issn":["0894-3370","1099-1204"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Numerical Modelling: Electronic Networks, Devices and Fields","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/jnm.70200","doi":"https://doi.org/10.1002/jnm.70200","is_oa":true,"landing_page_url":"https://doi.org/10.1002/jnm.70200","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/jnm.70200","source":{"id":"https://openalex.org/S201890602","display_name":"International Journal of Numerical Modelling Electronic Networks Devices and Fields","issn_l":"0894-3370","issn":["0894-3370","1099-1204"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-40","russia-white-list-2"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Numerical Modelling: Electronic Networks, Devices and Fields","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208720927.pdf","grobid_xml":"https://content.openalex.org/works/W7208720927.grobid-xml"},"referenced_works_count":51,"referenced_works":["https://openalex.org/W637506955","https://openalex.org/W1560209300","https://openalex.org/W1583323312","https://openalex.org/W1991908582","https://openalex.org/W2005666831","https://openalex.org/W2007795813","https://openalex.org/W2010812143","https://openalex.org/W2016694818","https://openalex.org/W2021492437","https://openalex.org/W2031164264","https://openalex.org/W2031702332","https://openalex.org/W2041275200","https://openalex.org/W2060910778","https://openalex.org/W2103999702","https://openalex.org/W2104642800","https://openalex.org/W2145137020","https://openalex.org/W2171584085","https://openalex.org/W2183005587","https://openalex.org/W2190573361","https://openalex.org/W2198011566","https://openalex.org/W2509163710","https://openalex.org/W2557891946","https://openalex.org/W2565694081","https://openalex.org/W2594395784","https://openalex.org/W2619646298","https://openalex.org/W2622528340","https://openalex.org/W2793619583","https://openalex.org/W2799770891","https://openalex.org/W2802603505","https://openalex.org/W2810157381","https://openalex.org/W2887481719","https://openalex.org/W2888548938","https://openalex.org/W2902797372","https://openalex.org/W2919909604","https://openalex.org/W2940248389","https://openalex.org/W2948414694","https://openalex.org/W2948992794","https://openalex.org/W2949003516","https://openalex.org/W2999238115","https://openalex.org/W3014569360","https://openalex.org/W3032584751","https://openalex.org/W3081447890","https://openalex.org/W3083176014","https://openalex.org/W3097521549","https://openalex.org/W3097556928","https://openalex.org/W3151782210","https://openalex.org/W3159954016","https://openalex.org/W3171332058","https://openalex.org/W4206537305","https://openalex.org/W4289344822","https://openalex.org/W4406146708"],"related_works":["https://openalex.org/W4385691339","https://openalex.org/W4403603100","https://openalex.org/W4225532927","https://openalex.org/W3193439079","https://openalex.org/W7126269563","https://openalex.org/W4399049877","https://openalex.org/W2781710278","https://openalex.org/W3169362800","https://openalex.org/W2155980958","https://openalex.org/W4416594742"],"abstract_inverted_index":{"ABSTRACT":[0],"This":[1],"paper":[2],"presents":[3],"a":[4,58,103,121,137],"novel":[5],"stepwise":[6,59,105],"numerical":[7,38,157],"method":[8,44,152,177],"based":[9],"on":[10,99,188],"Fibonacci":[11,54,83,122],"wavelets":[12],"for":[13,81,185],"solving":[14],"fractional":[15,47,77],"stochastic":[16],"delay":[17,111],"differential":[18],"systems.":[19],"Such":[20],"systems":[21],"arise":[22],"in":[23],"numerous":[24],"applications":[25],"where":[26],"memory":[27],"effects,":[28],"randomness,":[29],"and":[30,34,146,159,167],"time":[31,72,190],"delays":[32],"coexist,":[33],"their":[35],"accurate":[36],"long\u2010time":[37],"treatment":[39],"remains":[40],"challenging.":[41],"The":[42,172],"proposed":[43,151],"combines":[45],"the":[46,53,75,82,94,110,116,130,134,150,165,170,176],"derivative":[48,78],"operational":[49,79,131],"matrices":[50],"associated":[51],"with":[52,57,67,129,161],"wavelet":[55,84,123],"basis":[56,85],"discretization":[60],"strategy,":[61],"thereby":[62],"integrating":[63],"high":[64],"spectral":[65],"accuracy":[66,180],"stable":[68],"computation":[69],"over":[70],"extended":[71],"intervals.":[73],"First,":[74],"arbitrary\u2010order":[76],"matrix":[80,132],"functions":[86],"is":[87,97,118],"constructed":[88],"via":[89],"block":[90],"pulse":[91],"functions.":[92],"Then,":[93],"original":[95],"problem":[96,135],"solved":[98],"successive":[100],"subintervals":[101],"using":[102],"recursive":[104],"procedure":[106],"that":[107,175],"efficiently":[108],"incorporates":[109],"term.":[112],"At":[113],"each":[114],"step,":[115],"solution":[117],"approximated":[119],"by":[120],"expansion;":[124],"applying":[125],"collocation":[126],"conditions":[127],"together":[128],"reduces":[133],"to":[136],"system":[138],"of":[139,149,169],"algebraic":[140],"equations.":[141],"A":[142],"rigorous":[143],"convergence":[144],"analysis":[145],"error":[147],"bounds":[148],"are":[153],"provided.":[154],"Finally,":[155],"several":[156],"examples":[158],"comparisons":[160],"existing":[162],"methods":[163],"demonstrate":[164],"efficiency":[166,184],"robustness":[168],"algorithm.":[171],"results":[173],"confirm":[174],"achieves":[178],"remarkable":[179],"while":[181],"maintaining":[182],"computational":[183],"problems":[186],"defined":[187],"long":[189],"domains.":[191]},"counts_by_year":[],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2026-09-05T00:00:00"}
