{"id":"https://openalex.org/W4409634219","doi":"https://doi.org/10.3390/axioms14040318","title":"Existence of Solutions for Caputo-Type Fractional (p,q)-Difference Equations Under Robin Boundary Conditions","display_name":"Existence of Solutions for Caputo-Type Fractional (p,q)-Difference Equations Under Robin Boundary Conditions","publication_year":2025,"publication_date":"2025-04-21","ids":{"openalex":"https://openalex.org/W4409634219","doi":"https://doi.org/10.3390/axioms14040318"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14040318","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040318","pdf_url":"https://www.mdpi.com/2075-1680/14/4/318/pdf?version=1745227252","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,"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"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/4/318/pdf?version=1745227252","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032840693","display_name":"Hui Ma","orcid":"https://orcid.org/0000-0002-5272-8226"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hailong Ma","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100402308","display_name":"Hongyu Li","orcid":"https://orcid.org/0000-0003-0795-9188"},"institutions":[{"id":"https://openalex.org/I80143920","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98","country_code":"CN","type":"education","lineage":["https://openalex.org/I80143920"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongyu Li","raw_affiliation_strings":["College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China","institution_ids":["https://openalex.org/I80143920"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100402308"],"corresponding_institution_ids":["https://openalex.org/I80143920"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11926407,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"318","last_page":"318"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976999759674072,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976999759674072,"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":0.9975000023841858,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9972000122070312,"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/type","display_name":"Type (biology)","score":0.737572431564331},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6504048109054565},{"id":"https://openalex.org/keywords/robin-boundary-condition","display_name":"Robin boundary condition","score":0.5700443387031555},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4578683376312256},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38460761308670044},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36932286620140076},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.13002237677574158},{"id":"https://openalex.org/keywords/geology","display_name":"Geology","score":0.047654151916503906}],"concepts":[{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.737572431564331},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6504048109054565},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.5700443387031555},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4578683376312256},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38460761308670044},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36932286620140076},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.13002237677574158},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.047654151916503906},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14040318","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040318","pdf_url":"https://www.mdpi.com/2075-1680/14/4/318/pdf?version=1745227252","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,"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:fc4c1d5681f0499ca18b1d934a88abfb","is_oa":true,"landing_page_url":"https://doaj.org/article/fc4c1d5681f0499ca18b1d934a88abfb","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 4, p 318 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14040318","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14040318","pdf_url":"https://www.mdpi.com/2075-1680/14/4/318/pdf?version=1745227252","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,"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":[],"awards":[{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2995223166","display_name":null,"funder_award_id":"12371173","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3829860627","display_name":null,"funder_award_id":"11801322","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G5636995342","display_name":null,"funder_award_id":"12371173","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6454507604","display_name":null,"funder_award_id":"11801322","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7438267050","display_name":null,"funder_award_id":"11801322;12371173","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8494410191","display_name":null,"funder_award_id":"ZR2021MA064","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4409634219.pdf","grobid_xml":"https://content.openalex.org/works/W4409634219.grobid-xml"},"referenced_works_count":40,"referenced_works":["https://openalex.org/W1981478955","https://openalex.org/W2013968512","https://openalex.org/W2017083850","https://openalex.org/W2027175213","https://openalex.org/W2052295270","https://openalex.org/W2074024269","https://openalex.org/W2111271983","https://openalex.org/W2116438794","https://openalex.org/W2119337296","https://openalex.org/W2148885158","https://openalex.org/W2326886507","https://openalex.org/W2790013524","https://openalex.org/W2902717265","https://openalex.org/W3030308006","https://openalex.org/W3031336767","https://openalex.org/W3177737292","https://openalex.org/W3201188940","https://openalex.org/W3207447652","https://openalex.org/W3215294569","https://openalex.org/W4200251348","https://openalex.org/W4235742176","https://openalex.org/W4237844826","https://openalex.org/W4240644230","https://openalex.org/W4293157724","https://openalex.org/W4298369610","https://openalex.org/W4307700588","https://openalex.org/W4310036597","https://openalex.org/W4367334803","https://openalex.org/W4382279236","https://openalex.org/W4383341839","https://openalex.org/W4393012143","https://openalex.org/W4396524889","https://openalex.org/W4400871769","https://openalex.org/W4400979821","https://openalex.org/W4402658569","https://openalex.org/W4403214754","https://openalex.org/W4404844716","https://openalex.org/W4404944967","https://openalex.org/W6872840921","https://openalex.org/W7066034450"],"related_works":["https://openalex.org/W3136311820","https://openalex.org/W1586418441","https://openalex.org/W1514481392","https://openalex.org/W1975751040","https://openalex.org/W2488633177","https://openalex.org/W4372049322","https://openalex.org/W2947472662","https://openalex.org/W2888445389","https://openalex.org/W2352708639","https://openalex.org/W2051519054"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,19,36,46],"investigate":[4],"the":[5,21,39,51,54],"existence":[6,22,40],"results":[7,41],"of":[8,42,53],"solutions":[9],"for":[10],"Caputo-type":[11],"fractional":[12],"(p,q)-difference":[13],"equations.":[14],"Using":[15],"Banach\u2019s":[16],"fixed-point":[17,30],"theorem,":[18],"obtain":[20,38],"and":[23,32],"uniqueness":[24],"results.":[25,56],"Meanwhile,":[26],"by":[27],"applying":[28],"Krasnoselskii\u2019s":[29],"theorem":[31],"Leray-Schauder\u2019s":[33],"nonlinear":[34],"alternative,":[35],"also":[37],"non-trivial":[43],"solutions.":[44],"Finally,":[45],"provide":[47],"examples":[48],"to":[49],"verify":[50],"correctness":[52],"given":[55],"Moreover,":[57],"relevant":[58],"applications":[59],"are":[60],"presented":[61],"through":[62],"specific":[63],"examples.":[64]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-04-22T00:00:00"}