{"id":"https://openalex.org/W2781719007","doi":"https://doi.org/10.1155/2018/8918541","title":"Computational Analysis of Complex Population Dynamical Model with Arbitrary Order","display_name":"Computational Analysis of Complex Population Dynamical Model with Arbitrary Order","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2781719007","doi":"https://doi.org/10.1155/2018/8918541","mag":"2781719007"},"language":"en","primary_location":{"id":"doi:10.1155/2018/8918541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/8918541","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/8918541.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":"http://downloads.hindawi.com/journals/complexity/2018/8918541.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101937507","display_name":"Fazal Haq","orcid":"https://orcid.org/0000-0002-6981-2782"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Fazal Haq","raw_affiliation_strings":["Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa, Pakistan","Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]},{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa","institution_ids":["https://openalex.org/I263208278"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073895350","display_name":"Kamal Shah","orcid":"https://orcid.org/0000-0002-8851-4844"},"institutions":[{"id":"https://openalex.org/I68649149","display_name":"University of Malakand","ror":"https://ror.org/012xdha97","country_code":"PK","type":"education","lineage":["https://openalex.org/I68649149"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Kamal Shah","raw_affiliation_strings":["Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan","Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I68649149"]},{"raw_affiliation_string":"Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa","institution_ids":["https://openalex.org/I68649149"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015298182","display_name":"Ghaus ur Rahman","orcid":"https://orcid.org/0000-0002-3168-181X"},"institutions":[{"id":"https://openalex.org/I335365548","display_name":"University of Swat","ror":"https://ror.org/01q9mqz67","country_code":"PK","type":"education","lineage":["https://openalex.org/I335365548"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Ghaus ur Rahman","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Swat, Mingora, Pakistan","Department of Mathematics and Statistics, University of Swat, Mingora"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Swat, Mingora, Pakistan","institution_ids":["https://openalex.org/I335365548"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Swat, Mingora","institution_ids":["https://openalex.org/I335365548"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101561342","display_name":"Yongjin Li","orcid":"https://orcid.org/0000-0003-4322-308X"},"institutions":[{"id":"https://openalex.org/I157773358","display_name":"Sun Yat-sen University","ror":"https://ror.org/0064kty71","country_code":"CN","type":"education","lineage":["https://openalex.org/I157773358"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yongjin Li","raw_affiliation_strings":["Department of Mathematics, Sun Yat-sen University, Guangzhou, China","Department of Mathematics, Sun Yat-sen University, Guangzhou"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University, Guangzhou, China","institution_ids":["https://openalex.org/I157773358"]},{"raw_affiliation_string":"Department of Mathematics, Sun Yat-sen University, Guangzhou","institution_ids":["https://openalex.org/I157773358"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005220352","display_name":"Muhammad Shahzad","orcid":"https://orcid.org/0000-0002-2290-804X"},"institutions":[{"id":"https://openalex.org/I263208278","display_name":"Hazara University","ror":"https://ror.org/018y22094","country_code":"PK","type":"education","lineage":["https://openalex.org/I263208278"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Shahzad","raw_affiliation_strings":["Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa, Pakistan","Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa, Pakistan","institution_ids":["https://openalex.org/I263208278"]},{"raw_affiliation_string":"Department of Mathematics, Hazara University Mansehra, Khyber Pakhtunkhwa","institution_ids":["https://openalex.org/I263208278"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101561342"],"corresponding_institution_ids":["https://openalex.org/I157773358"],"apc_list":{"value":2300,"currency":"USD","value_usd":2300},"apc_paid":{"value":2300,"currency":"USD","value_usd":2300},"fwci":0.6667,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.66046916,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"2018","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T10482","display_name":"Mathematical and Theoretical Epidemiology and Ecology Models","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2739","display_name":"Public Health, Environmental and Occupational Health"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9628999829292297,"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/laplace-transform","display_name":"Laplace transform","score":0.7268194556236267},{"id":"https://openalex.org/keywords/adomian-decomposition-method","display_name":"Adomian decomposition method","score":0.6957023739814758},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5882036685943604},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5827723145484924},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5809198021888733},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5537678003311157},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5390007495880127},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.5121262073516846},{"id":"https://openalex.org/keywords/population","display_name":"Population","score":0.48288893699645996},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4645020663738251},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46413442492485046},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4407125413417816},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.42230290174484253},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34748998284339905},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2738303542137146},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25428396463394165},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2178858518600464}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7268194556236267},{"id":"https://openalex.org/C120317633","wikidata":"https://www.wikidata.org/wiki/Q3042796","display_name":"Adomian decomposition method","level":3,"score":0.6957023739814758},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5882036685943604},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5827723145484924},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5809198021888733},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5537678003311157},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5390007495880127},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.5121262073516846},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.48288893699645996},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4645020663738251},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46413442492485046},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4407125413417816},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.42230290174484253},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34748998284339905},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2738303542137146},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25428396463394165},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2178858518600464},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C149923435","wikidata":"https://www.wikidata.org/wiki/Q37732","display_name":"Demography","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2018/8918541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/8918541","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/8918541.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:8918541","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/8503/2018/8918541.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:d0aa646d1b85460cbfd4a4a1887ac9ec","is_oa":true,"landing_page_url":"https://doaj.org/article/d0aa646d1b85460cbfd4a4a1887ac9ec","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 2018 (2018)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2018/8918541","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2018/8918541","pdf_url":"http://downloads.hindawi.com/journals/complexity/2018/8918541.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/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/G2373731922","display_name":null,"funder_award_id":"115713","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/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/G6846881997","display_name":null,"funder_award_id":"(11571378)","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8496960304","display_name":null,"funder_award_id":"11571378","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2781719007.pdf","grobid_xml":"https://content.openalex.org/works/W2781719007.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W613721056","https://openalex.org/W1528987510","https://openalex.org/W1530054495","https://openalex.org/W1974763075","https://openalex.org/W1975838271","https://openalex.org/W1979294065","https://openalex.org/W2007380962","https://openalex.org/W2021591459","https://openalex.org/W2047865461","https://openalex.org/W2049829830","https://openalex.org/W2116987651","https://openalex.org/W2186437051","https://openalex.org/W2298140078","https://openalex.org/W2592872439","https://openalex.org/W2596494212","https://openalex.org/W2745324256","https://openalex.org/W2963641381","https://openalex.org/W4240465921"],"related_works":["https://openalex.org/W4313233315","https://openalex.org/W2109023520","https://openalex.org/W3095724723","https://openalex.org/W1586145079","https://openalex.org/W4281619695","https://openalex.org/W2901432230","https://openalex.org/W2048436983","https://openalex.org/W2233017382","https://openalex.org/W2523462812","https://openalex.org/W1864123311"],"abstract_inverted_index":{"This":[0],"paper":[1],"considers":[2],"the":[3,20,54,67,70],"approximation":[4],"of":[5,39,56,69,85],"solution":[6,52],"for":[7,81],"a":[8,32,43,51],"fractional":[9,15],"order":[10,41],"biological":[11],"population":[12],"model.":[13],"The":[14,46,72],"derivative":[16],"is":[17,77],"considered":[18,47],"in":[19,42,53],"Caputo":[21],"sense.":[22],"By":[23],"using":[24],"Laplace":[25],"Adomian":[26],"decomposition":[27],"method":[28],"(LADM),":[29],"we":[30],"construct":[31],"base":[33],"function":[34],"and":[35,79],"provide":[36],"deformation":[37],"equation":[38],"higher":[40],"simple":[44],"equation.":[45],"scheme":[48],"gives":[49],"us":[50],"form":[55],"rapidly":[57],"convergent":[58],"infinite":[59],"series.":[60],"Some":[61],"examples":[62],"are":[63],"used":[64],"to":[65],"show":[66,74],"efficiency":[68],"method.":[71],"results":[73],"that":[75],"LADM":[76],"efficient":[78],"accurate":[80],"solving":[82],"such":[83],"types":[84],"nonlinear":[86],"problems.":[87]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
