{"id":"https://openalex.org/W3203189114","doi":"https://doi.org/10.1007/s40314-021-01649-6","title":"On numerical simulations of time fractional Phi-four equation using Caputo derivative","display_name":"On numerical simulations of time fractional Phi-four equation using Caputo derivative","publication_year":2021,"publication_date":"2021-09-30","ids":{"openalex":"https://openalex.org/W3203189114","doi":"https://doi.org/10.1007/s40314-021-01649-6","mag":"3203189114"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01649-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01649-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035360533","display_name":"Mohsin Kamran","orcid":null},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]},{"id":"https://openalex.org/I5100685","display_name":"University of Education","ror":"https://ror.org/052z7nw84","country_code":"PK","type":"education","lineage":["https://openalex.org/I5100685"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Mohsin Kamran","raw_affiliation_strings":["Department of Mathematics, Division of Science and Technology,  University of Education Lahore, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Division of Science and Technology,  University of Education Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I3130814776","https://openalex.org/I5100685"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043280787","display_name":"Abdul Majeed","orcid":"https://orcid.org/0000-0002-0316-1585"},"institutions":[{"id":"https://openalex.org/I3130814776","display_name":"University of Okara","ror":"https://ror.org/02fmg6q11","country_code":"PK","type":"education","lineage":["https://openalex.org/I3130814776"]},{"id":"https://openalex.org/I5100685","display_name":"University of Education","ror":"https://ror.org/052z7nw84","country_code":"PK","type":"education","lineage":["https://openalex.org/I5100685"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Abdul Majeed","raw_affiliation_strings":["Department of Mathematics, Division of Science and Technology,  University of Education Lahore, Lahore, Pakistan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Division of Science and Technology,  University of Education Lahore, Lahore, Pakistan","institution_ids":["https://openalex.org/I3130814776","https://openalex.org/I5100685"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100615345","display_name":"Jing Li","orcid":"https://orcid.org/0000-0002-7278-2764"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]},{"id":"https://openalex.org/I4210117825","display_name":"Beijing Research Institute of Mechanical and Electrical Technology","ror":"https://ror.org/02bjnsn63","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210117825"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing Li","raw_affiliation_strings":["Faculty of Science, Interdisciplinary Research Institute, Beijing University of Technology, Beijing, 100124, People\u2019s Republic of China","Faculty of Science, Interdisciplinary Research Institute, Beijing University of Technology, Beijing, 100124, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Science, Interdisciplinary Research Institute, Beijing University of Technology, Beijing, 100124, People\u2019s Republic of China","institution_ids":["https://openalex.org/I37796252","https://openalex.org/I4210117825"]},{"raw_affiliation_string":"Faculty of Science, Interdisciplinary Research Institute, Beijing University of Technology, Beijing, 100124, People's Republic of China","institution_ids":["https://openalex.org/I37796252"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5043280787"],"corresponding_institution_ids":["https://openalex.org/I3130814776","https://openalex.org/I5100685"],"apc_list":{"value":3090,"currency":"USD","value_usd":3090},"apc_paid":null,"fwci":0.5066,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.60864297,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"40","issue":"7","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":0.9998999834060669,"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":0.9998999834060669,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9830999970436096,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7645518779754639},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6558413505554199},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6090310215950012},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5855937004089355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48833200335502625},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48564329743385315},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.44594940543174744},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4415154457092285}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7645518779754639},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6558413505554199},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6090310215950012},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5855937004089355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48833200335502625},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48564329743385315},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.44594940543174744},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4415154457092285}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01649-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01649-6","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"0101-8205","issn":["0101-8205","1807-0302","2238-3603"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W1500601100","https://openalex.org/W1540790429","https://openalex.org/W1968458248","https://openalex.org/W1989835885","https://openalex.org/W2010132988","https://openalex.org/W2015696140","https://openalex.org/W2016437866","https://openalex.org/W2024509978","https://openalex.org/W2054040173","https://openalex.org/W2067140462","https://openalex.org/W2072177053","https://openalex.org/W2084797093","https://openalex.org/W2086461451","https://openalex.org/W2095213543","https://openalex.org/W2267396220","https://openalex.org/W2336711932","https://openalex.org/W2346695849","https://openalex.org/W2416756981","https://openalex.org/W2555767520","https://openalex.org/W2604963227","https://openalex.org/W2609270331","https://openalex.org/W2609804191","https://openalex.org/W2761447101","https://openalex.org/W2766416637","https://openalex.org/W2768683914","https://openalex.org/W2769188192","https://openalex.org/W2787959293","https://openalex.org/W2793464511","https://openalex.org/W2885819609","https://openalex.org/W2890308695","https://openalex.org/W2907239900","https://openalex.org/W2945322382","https://openalex.org/W2971186194","https://openalex.org/W2973204085","https://openalex.org/W3011893726","https://openalex.org/W3029286769","https://openalex.org/W3031653049","https://openalex.org/W3034627546","https://openalex.org/W3041434406","https://openalex.org/W3045659611","https://openalex.org/W3049382071","https://openalex.org/W3082486558","https://openalex.org/W3088926702","https://openalex.org/W3092373418","https://openalex.org/W3096611353","https://openalex.org/W3104152338","https://openalex.org/W3127534953","https://openalex.org/W3132699400","https://openalex.org/W3134110295","https://openalex.org/W3137905712","https://openalex.org/W3162676887","https://openalex.org/W3165874078","https://openalex.org/W4231574942","https://openalex.org/W4247465432"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W3154385886","https://openalex.org/W3000218850","https://openalex.org/W2161513111","https://openalex.org/W912076904","https://openalex.org/W3164740183","https://openalex.org/W2525556503"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}