{"id":"https://openalex.org/W4309708732","doi":"https://doi.org/10.3390/axioms11110655","title":"Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions","display_name":"Certain New Class of Analytic Functions Defined by Using a Fractional Derivative and Mittag-Leffler Functions","publication_year":2022,"publication_date":"2022-11-18","ids":{"openalex":"https://openalex.org/W4309708732","doi":"https://doi.org/10.3390/axioms11110655"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11110655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110655","pdf_url":"https://www.mdpi.com/2075-1680/11/11/655/pdf?version=1669099327","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/2075-1680/11/11/655/pdf?version=1669099327","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066920839","display_name":"Mohammad Faisal Khan","orcid":"https://orcid.org/0000-0001-5053-5028"},"institutions":[{"id":"https://openalex.org/I120238654","display_name":"Saudi Electronic University","ror":"https://ror.org/05ndh7v49","country_code":"SA","type":"education","lineage":["https://openalex.org/I120238654"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Mohammad Faisal Khan","raw_affiliation_strings":["Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-5053-5028","affiliations":[{"raw_affiliation_string":"Department of Basic Science, College of Science and Theoretical Studies, Saudi Electronic University, Riyadh 11673, Saudi Arabia","institution_ids":["https://openalex.org/I120238654"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088682741","display_name":"Shahid Khan","orcid":"https://orcid.org/0000-0003-0361-4887"},"institutions":[{"id":"https://openalex.org/I3131573596","display_name":"Abbottabad University of Science and Technology","ror":"https://ror.org/0549hdw45","country_code":"PK","type":"education","lineage":["https://openalex.org/I3131573596"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Shahid Khan","raw_affiliation_strings":["Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan"],"raw_orcid":"https://orcid.org/0000-0003-0361-4887","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad 22500, Pakistan","institution_ids":["https://openalex.org/I3131573596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045073924","display_name":"Saqib Hussain","orcid":"https://orcid.org/0000-0002-8174-8795"},"institutions":[{"id":"https://openalex.org/I3131573596","display_name":"Abbottabad University of Science and Technology","ror":"https://ror.org/0549hdw45","country_code":"PK","type":"education","lineage":["https://openalex.org/I3131573596"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saqib Hussain","raw_affiliation_strings":["Department of Mathematics, COMSATS University, Abbottabad Campus, Abbottabad 22060, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University, Abbottabad Campus, Abbottabad 22060, Pakistan","institution_ids":["https://openalex.org/I3131573596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018818902","display_name":"Maslina Darus","orcid":"https://orcid.org/0000-0001-9138-916X"},"institutions":[{"id":"https://openalex.org/I885383172","display_name":"National University of Malaysia","ror":"https://ror.org/00bw8d226","country_code":"MY","type":"education","lineage":["https://openalex.org/I885383172"]}],"countries":["MY"],"is_corresponding":false,"raw_author_name":"Maslina Darus","raw_affiliation_strings":["Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia"],"raw_orcid":"https://orcid.org/0000-0001-9138-916X","affiliations":[{"raw_affiliation_string":"Department of Mathematical Science, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Malaysia","institution_ids":["https://openalex.org/I885383172"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5068483750","display_name":"Khaled Matarneh","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139873","display_name":"Arab Open University","ror":"https://ror.org/03vfnky71","country_code":"SA","type":"education","lineage":["https://openalex.org/I4210093932","https://openalex.org/I4210139873"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Khaled Matarneh","raw_affiliation_strings":["Faculity of Computer Science, Arab Open University, Riyadh 11681, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculity of Computer Science, Arab Open University, Riyadh 11681, Saudi Arabia","institution_ids":["https://openalex.org/I4210139873"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088682741"],"corresponding_institution_ids":["https://openalex.org/I3131573596"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8025,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71026199,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"11","issue":"11","first_page":"655","last_page":"655"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11822","display_name":"Analytic and geometric function theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11822","display_name":"Analytic and geometric function theory","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9970999956130981,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9959999918937683,"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/fractional-calculus","display_name":"Fractional calculus","score":0.912054181098938},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6618142127990723},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.632077693939209},{"id":"https://openalex.org/keywords/analytic-function","display_name":"Analytic function","score":0.6121636629104614},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5603585839271545},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.5580186247825623},{"id":"https://openalex.org/keywords/unit-disk","display_name":"Unit disk","score":0.549642026424408},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4944877624511719},{"id":"https://openalex.org/keywords/mittag-leffler-function","display_name":"Mittag-Leffler function","score":0.47087109088897705},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4578898847103119},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38465142250061035},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3745228052139282},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3700971007347107},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32758092880249023},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15735143423080444}],"concepts":[{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.912054181098938},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6618142127990723},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.632077693939209},{"id":"https://openalex.org/C205979905","wikidata":"https://www.wikidata.org/wiki/Q215084","display_name":"Analytic function","level":2,"score":0.6121636629104614},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5603585839271545},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.5580186247825623},{"id":"https://openalex.org/C47177299","wikidata":"https://www.wikidata.org/wiki/Q2390323","display_name":"Unit disk","level":2,"score":0.549642026424408},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4944877624511719},{"id":"https://openalex.org/C98724732","wikidata":"https://www.wikidata.org/wiki/Q1935235","display_name":"Mittag-Leffler function","level":3,"score":0.47087109088897705},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4578898847103119},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38465142250061035},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3745228052139282},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3700971007347107},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32758092880249023},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15735143423080444},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11110655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110655","pdf_url":"https://www.mdpi.com/2075-1680/11/11/655/pdf?version=1669099327","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:5f2881ab05e042f38612c64e6f85df85","is_oa":true,"landing_page_url":"https://doaj.org/article/5f2881ab05e042f38612c64e6f85df85","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 11, p 655 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/11/655/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11110655","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 11; Pages: 655","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11110655","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11110655","pdf_url":"https://www.mdpi.com/2075-1680/11/11/655/pdf?version=1669099327","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4309708732.pdf","grobid_xml":"https://content.openalex.org/works/W4309708732.grobid-xml"},"referenced_works_count":10,"referenced_works":["https://openalex.org/W1950030264","https://openalex.org/W1968849744","https://openalex.org/W2023141419","https://openalex.org/W2085082416","https://openalex.org/W2091714372","https://openalex.org/W2111360325","https://openalex.org/W2138456947","https://openalex.org/W2143289501","https://openalex.org/W2321709382","https://openalex.org/W4233886660"],"related_works":["https://openalex.org/W3004228824","https://openalex.org/W3133884202","https://openalex.org/W3026107561","https://openalex.org/W2003343126","https://openalex.org/W2788174946","https://openalex.org/W3168359935","https://openalex.org/W3136298996","https://openalex.org/W4312341257","https://openalex.org/W4309708732","https://openalex.org/W4295102634"],"abstract_inverted_index":{"Fractional":[0],"calculus":[1],"has":[2],"a":[3,48,56,66],"number":[4],"of":[5,10,22,29,51,59,65,74],"applications":[6,21],"in":[7,13,26,79],"the":[8,27,36,41],"field":[9,28],"science,":[11],"specially":[12],"mathematics.":[14],"In":[15],"this":[16],"paper,":[17],"we":[18,34],"discuss":[19,72],"some":[20,73],"fractional":[23,37,52,69],"differential":[24,38],"operators":[25],"geometric":[30,77],"function":[31],"theory.":[32],"Here,":[33],"combine":[35],"operator":[39,50,70],"and":[40,46,71],"Mittag-Leffler":[42],"functions":[43,62],"to":[44],"formulate":[45],"arrange":[47],"new":[49,57],"calculus.":[53],"We":[54],"define":[55],"class":[58],"normalized":[60],"analytic":[61],"by":[63],"means":[64],"newly":[67],"defined":[68],"its":[75],"interesting":[76],"properties":[78],"open":[80],"unit":[81],"disk.":[82]},"counts_by_year":[{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
