{"id":"https://openalex.org/W7223287883","doi":"https://doi.org/10.3390/axioms15110792","title":"Fractional Stochastic Difference Systems: Well-Posedness, Stability, Perturbation Analysis, and Macroeconomic Application","display_name":"Fractional Stochastic Difference Systems: Well-Posedness, Stability, Perturbation Analysis, and Macroeconomic Application","publication_year":2026,"publication_date":"2026-10-22","ids":{"openalex":"https://openalex.org/W7223287883","doi":"https://doi.org/10.3390/axioms15110792"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15110792","doi":"https://doi.org/10.3390/axioms15110792","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15110792","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.3390/axioms15110792","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069906818","display_name":"Muhammad Imran Liaqat","orcid":"https://orcid.org/0000-0002-5732-9689","observed_orcids":["https://orcid.org/0000-0002-5732-9689"]},"institutions":[{"id":"https://openalex.org/I103703290","display_name":"Sakarya University","ror":"https://ror.org/04ttnw109","country_code":"TR","type":"education","lineage":["https://openalex.org/I103703290"]},{"id":"https://openalex.org/I43729321","display_name":"National College of Business Administration and Economics","ror":"https://ror.org/02my4wj17","country_code":"PK","type":"education","lineage":["https://openalex.org/I43729321"]}],"countries":["PK","TR"],"is_corresponding":false,"raw_author_name":"Muhammad Imran Liaqat","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey","Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan"],"raw_orcid":"https://orcid.org/0000-0002-5732-9689","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, Turkey","institution_ids":["https://openalex.org/I103703290"]},{"raw_affiliation_string":"Department of Mathematics, National College of Business Administration & Economics, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I43729321"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010728851","display_name":"Abdulaziz Khalid Alsharidi","orcid":"https://orcid.org/0009-0007-2527-7398","observed_orcids":["https://orcid.org/0009-0007-2527-7398"]},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":true,"raw_author_name":"Abdulaziz Khalid Alsharidi","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia"],"raw_orcid":"https://orcid.org/0009-0007-2527-7398","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010728851"],"corresponding_institution_ids":["https://openalex.org/I4626487"],"apc_list":{"value":2400,"currency":"CHF","value_usd":2896},"apc_paid":{"value":2400,"currency":"CHF","value_usd":2896},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.74266893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"11","first_page":"792","last_page":"792"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9839000105857849,"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"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9839000105857849,"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"}},{"id":"https://openalex.org/T12135","display_name":"Fuzzy Systems and Optimization","score":0.007300000172108412,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.006200000178068876,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/existence-and-uniqueness-of-solutions","display_name":"existence and uniqueness of solutions","score":0.7149999737739563},{"id":"https://openalex.org/keywords/mean-square-stability","display_name":"mean square stability","score":0.7950000166893005},{"id":"https://openalex.org/keywords/perturbation-analysis","display_name":"perturbation analysis","score":0.843999981880188},{"id":"https://openalex.org/keywords/picard-iteration","display_name":"Picard iteration","score":0.7279999852180481},{"id":"https://openalex.org/keywords/comparison-principle","display_name":"comparison principle","score":0.7429999709129333},{"id":"https://openalex.org/keywords/dissipativity","display_name":"dissipativity","score":0.8069999814033508},{"id":"https://openalex.org/keywords/mittag-leffler-stability","display_name":"Mittag-Leffler stability","score":0.9860000014305115},{"id":"https://openalex.org/keywords/macroeconomic-models","display_name":"macroeconomic models","score":0.6579999923706055},{"id":"https://openalex.org/keywords/fractional-order","display_name":"fractional order","score":0.3179999887943268},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.6179999709129333}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8950999975204468},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.599399983882904},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5992000102996826},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5817000269889832},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5353999733924866},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4456000030040741},{"id":"https://openalex.org/C186215838","wikidata":"https://www.wikidata.org/wiki/Q772232","display_name":"Conditional expectation","level":2,"score":0.42149999737739563},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.3528999984264374},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3375000059604645},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.3319000005722046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31610000133514404},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.28760001063346863},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.2809999883174896},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.26829999685287476},{"id":"https://openalex.org/C108819105","wikidata":"https://www.wikidata.org/wiki/Q1143293","display_name":"Fractional Brownian motion","level":3,"score":0.2662000060081482},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.2630999982357025},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.26269999146461487},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.25440001487731934},{"id":"https://openalex.org/C37608338","wikidata":"https://www.wikidata.org/wiki/Q510733","display_name":"Gronwall's inequality","level":3,"score":0.2533000111579895}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.3390/axioms15110792","doi":"https://doi.org/10.3390/axioms15110792","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15110792","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.3390/axioms15110792","doi":"https://doi.org/10.3390/axioms15110792","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15110792","pdf_url":null,"source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","poland-20","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1965801804","https://openalex.org/W1986866825","https://openalex.org/W2044165128","https://openalex.org/W2061452102","https://openalex.org/W2296779811","https://openalex.org/W3028895610","https://openalex.org/W4392755882","https://openalex.org/W4395667196","https://openalex.org/W4400118655","https://openalex.org/W4401474709","https://openalex.org/W4403214754","https://openalex.org/W7118326324","https://openalex.org/W7161176209","https://openalex.org/W7212291271"],"related_works":["https://openalex.org/W4406273026","https://openalex.org/W7110666825","https://openalex.org/W3189967048","https://openalex.org/W4322743049","https://openalex.org/W7208805618","https://openalex.org/W7204544675","https://openalex.org/W7221023697","https://openalex.org/W2013775066","https://openalex.org/W2893700337","https://openalex.org/W7171530587"],"abstract_inverted_index":{"We":[0,87],"investigate":[1],"nonlinear":[2,168],"Caputo\u2013nabla":[3,109],"fractional":[4,14,69,161],"stochastic":[5],"difference":[6],"systems":[7],"driven":[8],"by":[9],"independent":[10],"Gaussian":[11],"increments.":[12],"The":[13,71,130],"summation":[15],"identity":[16,124],"yields":[17],"an":[18,121],"exact":[19,122],"pathwise":[20,31],"Volterra":[21],"representation":[22],"whose":[23],"strictly":[24],"causal":[25],"structure":[26],"establishes":[27,147],"finite-horizon":[28,94],"existence":[29],"and":[30,35,50,64,67,80,97,119,151],"uniqueness":[32],"under":[33],"measurability":[34],"linear-growth":[36],"assumptions,":[37,46],"without":[38],"requiring":[39],"a":[40,137,142,155,167],"contraction":[41],"condition.":[42,129],"Under":[43],"global":[44],"Lipschitz":[45],"separate":[47],"weighted":[48],"\u21131":[49],"\u21132":[51],"kernel":[52],"estimates":[53,75],"provide":[54],"quantitative":[55],"mean-square":[56,149],"bounds":[57],"for":[58,125],"perturbations":[59],"of":[60,73,100,114],"initial":[61],"data,":[62],"drift":[63],"diffusion":[65],"coefficients,":[66],"the":[68,77,81,115,126,177],"order.":[70],"dependence":[72],"these":[74],"on":[76,136],"exponential":[78],"weight":[79],"observation":[82],"horizon":[83],"is":[84,152],"made":[85],"explicit.":[86],"also":[88],"establish":[89,112],"residual-based":[90],"Ulam-type":[91],"stability":[92,132,150],"estimates,":[93,175],"moment":[95],"bounds,":[96],"finite-step":[98],"exactness":[99],"Picard":[101],"iteration.":[102],"For":[103],"long-time":[104],"analysis,":[105],"we":[106],"prove":[107],"discrete":[108],"comparison":[110],"principles,":[111],"decay":[113],"associated":[116],"scalar":[117],"resolvent,":[118],"derive":[120],"quadratic":[123],"corresponding":[127],"dissipativity":[128,139],"Mittag\u2013Leffler":[131],"result":[133],"remains":[134],"conditional":[135],"history-dependent":[138],"inequality.":[140],"Independently,":[141],"directly":[143],"verifiable":[144],"coefficient-level":[145],"criterion":[146],"asymptotic":[148],"applied":[153],"to":[154],"three-dimensional":[156],"illustrative":[157],"macroeconomic":[158],"model":[159],"at":[160],"order":[162],"\u03d1=0.75.":[163],"Numerical":[164],"experiments,":[165],"including":[166],"Monte":[169],"Carlo":[170],"simulation":[171],"with":[172],"sampling":[173],"uncertainty":[174],"illustrate":[176],"theoretical":[178],"results.":[179]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-24T00:00:00"}