{"id":"https://openalex.org/W7215838220","doi":"https://doi.org/10.3390/axioms15100737","title":"Integral Contraction Approach to Coupled Integro-Fractional Stochastic Differential Systems","display_name":"Integral Contraction Approach to Coupled Integro-Fractional Stochastic Differential Systems","publication_year":2026,"publication_date":"2026-10-01","ids":{"openalex":"https://openalex.org/W7215838220","doi":"https://doi.org/10.3390/axioms15100737"},"language":"en","primary_location":{"id":"doi:10.3390/axioms15100737","doi":"https://doi.org/10.3390/axioms15100737","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15100737","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/axioms15100737","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/I43879129","display_name":"Government College University, Lahore","ror":"https://ror.org/040gec961","country_code":"PK","type":"education","lineage":["https://openalex.org/I43879129"]}],"countries":["PK","TR"],"is_corresponding":false,"raw_author_name":"Muhammad Imran Liaqat","raw_affiliation_strings":["Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan","Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, T\u00fcrkiye"],"raw_orcid":"https://orcid.org/0000-0002-5732-9689","affiliations":[{"raw_affiliation_string":"Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan","institution_ids":["https://openalex.org/I43879129"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Sakarya University, Sakarya 54050, T\u00fcrkiye","institution_ids":["https://openalex.org/I103703290"]}]},{"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":0.66748831,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"15","issue":"10","first_page":"737","last_page":"737"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9682999849319458,"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":0.9682999849319458,"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":0.017400000244379044,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.007000000216066837,"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/nonlocal-integral-boundary-conditions","display_name":"nonlocal integral boundary conditions","score":0.9480000138282776},{"id":"https://openalex.org/keywords/green-kernel","display_name":"Green kernel","score":0.6940000057220459},{"id":"https://openalex.org/keywords/hyers-ulam-stability","display_name":"Hyers-Ulam stability","score":0.9449999928474426},{"id":"https://openalex.org/keywords/non-lipschitz-coefficients","display_name":"non-Lipschitz coefficients","score":0.8849999904632568},{"id":"https://openalex.org/keywords/trajectory-control","display_name":"trajectory control","score":0.7179999947547913},{"id":"https://openalex.org/keywords/stochastic-boundary-value-problems","display_name":"stochastic boundary value problems","score":0.6790000200271606}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.840399980545044},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.5289999842643738},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4893999993801117},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48919999599456787},{"id":"https://openalex.org/C39943821","wikidata":"https://www.wikidata.org/wiki/Q506346","display_name":"Semimartingale","level":2,"score":0.4717999994754791},{"id":"https://openalex.org/C48406656","wikidata":"https://www.wikidata.org/wiki/Q534112","display_name":"Martingale (probability theory)","level":2,"score":0.4708999991416931},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.46399998664855957},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4185999929904938},{"id":"https://openalex.org/C51955184","wikidata":"https://www.wikidata.org/wiki/Q1545585","display_name":"Stochastic differential equation","level":2,"score":0.40299999713897705},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.3853999972343445},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.32409998774528503},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.304500013589859},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.3027999997138977},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.27410000562667847},{"id":"https://openalex.org/C58435881","wikidata":"https://www.wikidata.org/wiki/Q1868500","display_name":"Local martingale","level":3,"score":0.27160000801086426},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.27000001072883606},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C103275481","wikidata":"https://www.wikidata.org/wiki/Q6787889","display_name":"Matrix representation","level":3,"score":0.2687999904155731},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2669000029563904},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.259799987077713},{"id":"https://openalex.org/C49555168","wikidata":"https://www.wikidata.org/wiki/Q176583","display_name":"Stochastic matrix","level":3,"score":0.2565999925136566},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms15100737","doi":"https://doi.org/10.3390/axioms15100737","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15100737","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"},{"id":"pmh:oai:doaj.org/article:66752bc1f2f641d1abfcd2c6523365da","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/66752bc1f2f641d1abfcd2c6523365da","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 15, Iss 10, p 737 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms15100737","doi":"https://doi.org/10.3390/axioms15100737","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms15100737","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1963816763","https://openalex.org/W2047319220","https://openalex.org/W2136419055","https://openalex.org/W2563245034","https://openalex.org/W3092219476","https://openalex.org/W3207337363","https://openalex.org/W4210702327","https://openalex.org/W4283018994","https://openalex.org/W4315434950","https://openalex.org/W4403684313","https://openalex.org/W4404534299","https://openalex.org/W4408167983","https://openalex.org/W7155386826"],"related_works":["https://openalex.org/W4404901357","https://openalex.org/W4415872571","https://openalex.org/W7163886786","https://openalex.org/W4284975787","https://openalex.org/W7207558699","https://openalex.org/W2136419055","https://openalex.org/W4414711439","https://openalex.org/W3165518459","https://openalex.org/W4414823946","https://openalex.org/W4406363576"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,30,44,79,83,88,96,148,195],"coupled":[3,142],"system":[4],"of":[5,246],"Caputo\u2013Katugampola":[6],"integro\u2013fractional":[7],"stochastic":[8,197,252],"differential":[9],"equations":[10],"with":[11,78],"Volterra":[12],"memory,":[13],"nonlocal":[14],"integral":[15],"boundary":[16,56,62],"conditions,":[17],"Wiener":[18],"perturbations,":[19],"and":[20,64,82,131,153,203,234],"compensated":[21],"Poisson":[22],"jumps.":[23],"The":[24,119,141,239],"main":[25],"purpose":[26],"is":[27,50,91,123,145,157,166,192,200],"to":[28,93,110,137],"give":[29],"mathematically":[31],"explicit":[32,174],"fixed-point":[33,143],"treatment":[34],"in":[35,70,108],"which":[36],"the":[37,54,61,65,104,112,154,160,169,219,224,227,231,235,243,247,251],"two":[38,55],"components":[39],"are":[40,76,134],"solved":[41],"simultaneously":[42],"on":[43,103,115,139,218],"product":[45],"space.":[46],"A":[47,214],"Green":[48,67,221],"representation":[49,222],"derived":[51],"directly":[52],"from":[53,168,186],"conditions;":[57],"this":[58,190],"derivation":[59],"fixes":[60],"denominator":[63],"complete":[66],"kernel":[68],"used":[69,92,158],"all":[71,129],"subsequent":[72],"estimates.":[73],"Integral":[74],"contractors":[75],"formulated":[77],"correction":[80],"operator":[81],"residual":[84],"modulus.":[85],"In":[86],"particular,":[87],"cubic":[89],"nonlinearity":[90],"show":[94],"that":[95],"coefficient":[97],"need":[98],"not":[99],"be":[100],"globally":[101],"Lipschitz":[102],"whole":[105],"state":[106],"space":[107],"order":[109,121],"satisfy":[111],"contractor":[113,130,229],"hypothesis":[114],"an":[116,173,204],"invariant":[117],"ball.":[118],"moment":[120],"p\u22652":[122],"fixed":[124],"throughout":[125],"each":[126],"theorem,":[127],"so":[128],"contraction":[132,162,225],"constants":[133],"explicitly":[135],"allowed":[136],"depend":[138],"p.":[140],"problem":[144,199],"represented":[146],"by":[147,172],"nonnegative":[149],"2\u00d72":[150],"matrix":[151,171],"Qp":[152],"condition":[155],"\u03c1(Qp)<1":[156],"as":[159],"actual":[161],"condition.":[163],"Ulam\u2013Hyers":[164,232],"stability":[165],"obtained":[167],"same":[170,220],"Neumann-series":[175],"estimate.":[176],"For":[177],"trajectory":[178],"control":[179,207],"we":[180],"distinguish":[181],"ordinary":[182,205],"predictable":[183],"finite-energy":[184],"controls":[185],"generalized":[187,236],"semimartingale":[188],"controls;":[189],"distinction":[191],"necessary":[193],"because":[194],"two-point":[196],"boundary-value":[198],"generally":[201],"noncausal":[202],"drift":[206],"cannot":[208],"cancel":[209],"independent":[210],"martingale":[211],"terms":[212],"pathwise.":[213],"numerical":[215],"experiment":[216],"based":[217],"verifies":[223],"criterion,":[226],"non-Lipschitz":[228],"construction,":[230],"estimate,":[233],"trajectory-control":[237],"mechanism.":[238],"presentation":[240],"also":[241],"records":[242],"precise":[244],"scope":[245],"adaptedness":[248],"assumption":[249],"for":[250],"integrals.":[253]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-10-03T00:00:00"}
