{"id":"https://openalex.org/W3093185290","doi":"https://doi.org/10.1155/2020/8845867","title":"On Discrete Fractional Integral Inequalities for a Class of Functions","display_name":"On Discrete Fractional Integral Inequalities for a Class of Functions","publication_year":2020,"publication_date":"2020-10-19","ids":{"openalex":"https://openalex.org/W3093185290","doi":"https://doi.org/10.1155/2020/8845867","mag":"3093185290"},"language":"en","primary_location":{"id":"doi:10.1155/2020/8845867","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8845867","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8845867.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/complexity/2020/8845867.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091446521","display_name":"Saima Rashid","orcid":"https://orcid.org/0000-0001-7137-1720"},"institutions":[{"id":"https://openalex.org/I194348271","display_name":"Government College University, Faisalabad","ror":"https://ror.org/051zgra59","country_code":"PK","type":"education","lineage":["https://openalex.org/I194348271"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saima Rashid","raw_affiliation_strings":["Department of Mathematics, Government College University, Faisalabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I194348271"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114376646","display_name":"Hijaz Ahmad","orcid":"https://orcid.org/0000-0002-5438-5407"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Hijaz Ahmad","raw_affiliation_strings":["Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009763927","display_name":"Aasma Khalid","orcid":"https://orcid.org/0000-0003-4918-9732"},"institutions":[{"id":"https://openalex.org/I4210158239","display_name":"Government College Women University Faisalabad","ror":"https://ror.org/05rq0zy06","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210158239"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Aasma Khalid","raw_affiliation_strings":["Department of Mathematics, Government College Women University, Faisalabad, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Government College Women University, Faisalabad, Pakistan","institution_ids":["https://openalex.org/I4210158239"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046314241","display_name":"Yu\u2010Ming Chu","orcid":"https://orcid.org/0000-0002-0944-2134"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]},{"id":"https://openalex.org/I56934997","display_name":"Changsha University of Science and Technology","ror":"https://ror.org/03yph8055","country_code":"CN","type":"education","lineage":["https://openalex.org/I56934997"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Ming Chu","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou 313000, China","Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou 313000, China","institution_ids":["https://openalex.org/I3018263800"]},{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, China","institution_ids":["https://openalex.org/I56934997"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5046314241"],"corresponding_institution_ids":["https://openalex.org/I3018263800","https://openalex.org/I56934997"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.5953,"has_fulltext":true,"cited_by_count":17,"citation_normalized_percentile":{"value":0.75555671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"2020","issue":null,"first_page":"1","last_page":"13"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9994000196456909,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9811000227928162,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.970300018787384,"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/mathematics","display_name":"Mathematics","score":0.679461658000946},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5467398166656494},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5339272022247314},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.49910402297973633},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.4496666193008423},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4455721974372864},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.42577847838401794},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3863077759742737},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37250766158103943},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35738593339920044},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34487685561180115},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3189052939414978},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1849919855594635},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1268843114376068},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.09014809131622314}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.679461658000946},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5467398166656494},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5339272022247314},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.49910402297973633},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.4496666193008423},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4455721974372864},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.42577847838401794},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3863077759742737},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37250766158103943},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35738593339920044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34487685561180115},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3189052939414978},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1849919855594635},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1268843114376068},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.09014809131622314},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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:10.1155/2020/8845867","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8845867","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8845867.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:complx:8845867","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2020/8845867.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"pmh:oai:doaj.org/article:05a86936a94743d2b8d4f6d839ae7995","is_oa":true,"landing_page_url":"https://doaj.org/article/05a86936a94743d2b8d4f6d839ae7995","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Complexity, Vol 2020 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2020/8845867","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2020/8845867","pdf_url":"https://downloads.hindawi.com/journals/complexity/2020/8845867.pdf","source":{"id":"https://openalex.org/S207319443","display_name":"Complexity","issn_l":"1076-2787","issn":["1076-2787","1099-0526"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Complexity","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1064001500","display_name":null,"funder_award_id":"61673169","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"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/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/G37568934","display_name":null,"funder_award_id":"Grant","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"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3093185290.pdf","grobid_xml":"https://content.openalex.org/works/W3093185290.grobid-xml"},"referenced_works_count":52,"referenced_works":["https://openalex.org/W151388762","https://openalex.org/W1879346481","https://openalex.org/W1984646847","https://openalex.org/W1997844385","https://openalex.org/W2019823075","https://openalex.org/W2031064583","https://openalex.org/W2044165128","https://openalex.org/W2061452102","https://openalex.org/W2063067239","https://openalex.org/W2077736465","https://openalex.org/W2080931732","https://openalex.org/W2103022721","https://openalex.org/W2296779811","https://openalex.org/W2506955103","https://openalex.org/W2516066015","https://openalex.org/W2556794753","https://openalex.org/W2609774349","https://openalex.org/W2754952441","https://openalex.org/W2772531879","https://openalex.org/W2883444645","https://openalex.org/W2885016653","https://openalex.org/W2893921955","https://openalex.org/W2906702243","https://openalex.org/W2956087427","https://openalex.org/W2966090337","https://openalex.org/W2970687766","https://openalex.org/W2979628066","https://openalex.org/W2984489738","https://openalex.org/W2988561493","https://openalex.org/W2990568942","https://openalex.org/W2992434471","https://openalex.org/W2995915696","https://openalex.org/W3000399847","https://openalex.org/W3003199273","https://openalex.org/W3007601095","https://openalex.org/W3011438240","https://openalex.org/W3019255396","https://openalex.org/W3022237750","https://openalex.org/W3028969026","https://openalex.org/W3030631368","https://openalex.org/W3033589593","https://openalex.org/W3035400631","https://openalex.org/W3040578767","https://openalex.org/W3040789250","https://openalex.org/W3043648769","https://openalex.org/W3043747504","https://openalex.org/W3044249570","https://openalex.org/W3047289956","https://openalex.org/W3083176014","https://openalex.org/W3083513500","https://openalex.org/W3086128671","https://openalex.org/W3100222141"],"related_works":["https://openalex.org/W2229925025","https://openalex.org/W1539596337","https://openalex.org/W33469805","https://openalex.org/W1855007440","https://openalex.org/W2788247819","https://openalex.org/W2914699178","https://openalex.org/W4301243416","https://openalex.org/W2024985363","https://openalex.org/W2156911440","https://openalex.org/W3215334366"],"abstract_inverted_index":{"Discrete":[0],"fractional":[1,41,60,133,178,212],"calculus":[2],"<a:math":[3],"xmlns:a=\"http://www.w3.org/1998/Math/MathML\"":[4],"id=\"M1\">":[5],"<a:mfenced":[6],"open=\"(\"":[7,148],"close=\")\"":[8,149],"separators=\"|\">":[9,150],"<a:mrow>":[10],"<a:mi>\u2131</a:mi>":[11],"<a:mi":[12],"mathvariant=\"script\">C</a:mi>":[13],"</a:mrow>":[14],"</a:mfenced>":[15],"</a:math>":[16],"is":[17,93],"proposed":[18],"to":[19,30,183,191],"depict":[20],"neural":[21],"systems":[22],"with":[23],"memory":[24],"impacts.":[25],"This":[26],"research":[27],"article":[28],"aims":[29],"investigate":[31],"the":[32,35,38,54,57,64,98,119,124,129,171,188,199,204],"consequences":[33],"in":[34,53,85,170],"frame":[36],"of":[37,56,91,97,117,123,131,140,174,176,206,211],"discrete":[39,132,177],"proportional":[40],"operator.":[42],"<g:math":[43],"xmlns:g=\"http://www.w3.org/1998/Math/MathML\"":[44],"id=\"M2\">":[45],"<g:mi>\u210f</g:mi>":[46],"</g:math>":[47],"-discrete":[48],"exponential":[49],"functions":[50,142],"are":[51,83,159],"assumed":[52],"kernel":[55],"novel":[58],"generalized":[59],"sum":[61],"defined":[62],"on":[63,128,198],"time":[65],"scale":[66],"<i:math":[67],"xmlns:i=\"http://www.w3.org/1998/Math/MathML\"":[68],"id=\"M3\">":[69],"<i:mi>\u210f</i:mi>":[70],"<i:mi>\u2124</i:mi>":[71],"</i:math>":[72],".":[73],"The":[74,87],"nabla":[75],"<k:math":[76],"xmlns:k=\"http://www.w3.org/1998/Math/MathML\"":[77],"id=\"M4\">":[78],"<k:mi>\u210f</k:mi>":[79],"</k:math>":[80],"-fractional":[81],"sums":[82],"accounted":[84],"particular.":[86],"governing":[88],"high":[89],"discretization":[90],"problems":[92,210],"an":[94],"advanced":[95],"version":[96],"existing":[99],"forms":[100],"that":[101],"can":[102,163,186],"be":[103,164],"transformed":[104],"into":[105],"linear":[106],"and":[107,195],"nonlinear":[108],"difference":[109,179,213],"equations":[110],"using":[111],"appropriately":[112],"adjusted":[113],"transformations":[114],"invoking":[115],"property":[116],"observing":[118],"new":[120],"chaotic":[121],"behaviors":[122],"logistic":[125],"map.":[126],"Based":[127],"theory":[130],"calculus,":[134],"explicit":[135],"bounds":[136],"for":[137,203],"a":[138,167],"class":[139],"positive":[141],"<m:math":[143],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\"":[144],"id=\"M5\">":[145],"<m:mi>n</m:mi>":[146,152],"<m:mfenced":[147],"<m:mrow>":[151],"<m:mo>\u2208</m:mo>":[153],"<m:mi>\u2115</m:mi>":[154],"</m:mrow>":[155],"</m:mfenced>":[156],"</m:math>":[157],"concerned":[158],"established.":[160],"These":[161],"variants":[162],"utilized":[165],"as":[166],"convenient":[168],"apparatus":[169],"qualitative":[172],"analysis":[173],"solutions":[175,205],"equations.":[180,214],"With":[181],"respect":[182],"applications,":[184],"we":[185],"apply":[187],"introduced":[189],"outcomes":[190],"explore":[192],"boundedness,":[193],"uniqueness,":[194],"continuous":[196],"reliance":[197],"initial":[200],"value":[201],"problem":[202],"certain":[207],"underlying":[208],"worth":[209]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":4}],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-10-10T00:00:00"}
