{"id":"https://openalex.org/W2775976996","doi":"https://doi.org/10.1016/j.rinp.2017.12.051","title":"Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations","display_name":"Analytic solution for the space-time fractional Klein-Gordon and coupled conformable Boussinesq equations","publication_year":2017,"publication_date":"2017-12-20","ids":{"openalex":"https://openalex.org/W2775976996","doi":"https://doi.org/10.1016/j.rinp.2017.12.051","mag":"2775976996"},"language":"en","primary_location":{"id":"doi:10.1016/j.rinp.2017.12.051","doi":"https://doi.org/10.1016/j.rinp.2017.12.051","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2017.12.051","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379717322003/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.sciencedirect.com/science/article/pii/S2211379717322003/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086002310","display_name":"Muhannad A. Shallal","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I102254642","display_name":"University of Kirkuk","ror":"https://ror.org/01pk8rb11","country_code":"IQ","type":"education","lineage":["https://openalex.org/I102254642"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Muhannad A. Shallal","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq","institution_ids":["https://openalex.org/I102254642"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028208382","display_name":"Hawraz Nadhim Jabbar","orcid":"https://orcid.org/0000-0001-6867-8027","observed_orcids":["https://orcid.org/0000-0001-6867-8027"]},"institutions":[{"id":"https://openalex.org/I102254642","display_name":"University of Kirkuk","ror":"https://ror.org/01pk8rb11","country_code":"IQ","type":"education","lineage":["https://openalex.org/I102254642"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Hawraz N. Jabbar","raw_affiliation_strings":["Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Science, University of Kirkuk, Kirkuk, Iraq","institution_ids":["https://openalex.org/I102254642"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046780814","display_name":"Khalid K. Ali","orcid":"https://orcid.org/0000-0002-7801-2760","observed_orcids":["https://orcid.org/0000-0002-7801-2760"]},"institutions":[{"id":"https://openalex.org/I184834183","display_name":"Al-Azhar University","ror":"https://ror.org/05fnp1145","country_code":"EG","type":"education","lineage":["https://openalex.org/I184834183"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Khalid K. Ali","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Al-Azhar University, Nasr-City, Cairo, Egypt","institution_ids":["https://openalex.org/I184834183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046780814"],"corresponding_institution_ids":["https://openalex.org/I184834183"],"apc_list":{"value":1920,"currency":"USD","value_usd":1920},"apc_paid":{"value":1920,"currency":"USD","value_usd":1920},"fwci":5.1214,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.95244474,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":100},"biblio":{"volume":"8","issue":null,"first_page":"372","last_page":"378"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9613999724388123,"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":0.9613999724388123,"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":0.032999999821186066,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.0013000000035390258,"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/traveling-wave-solutions","display_name":"traveling wave solutions","score":0.9430000185966492},{"id":"https://openalex.org/keywords/analytical-solution","display_name":"analytical solution","score":0.8889999985694885},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.9879999756813049},{"id":"https://openalex.org/keywords/fractional-complex-transform","display_name":"fractional complex transform","score":0.8709999918937683},{"id":"https://openalex.org/keywords/modified-riemann-liouville-derivative","display_name":"modified Riemann-Liouville derivative","score":0.9490000009536743}],"concepts":[{"id":"https://openalex.org/C86072612","wikidata":"https://www.wikidata.org/wiki/Q5160239","display_name":"Conformable matrix","level":2,"score":0.8372573256492615},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6193188428878784},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6150004863739014},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6025072336196899},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.578766942024231},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5474385619163513},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4967702031135559},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.47396156191825867},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.4161667227745056},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.36667346954345703},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2518346905708313},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","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/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1016/j.rinp.2017.12.051","doi":"https://doi.org/10.1016/j.rinp.2017.12.051","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2017.12.051","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379717322003/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f9ef05c14b9f4e03901597e6ed915e00","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/f9ef05c14b9f4e03901597e6ed915e00","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,"listed_in":[],"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":"Results in Physics, Vol 8, Iss , Pp 372-378 (2018)","raw_type":"article"},{"id":"doi:10.60692/pxrnj-cnm06","doi":"https://doi.org/10.60692/pxrnj-cnm06","is_oa":true,"landing_page_url":"https://doi.org/10.60692/pxrnj-cnm06","pdf_url":null,"source":{"id":"https://openalex.org/S7407051682","display_name":"Greater South Information System","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"},{"id":"doi:10.60692/y1fs0-97s73","doi":"https://doi.org/10.60692/y1fs0-97s73","is_oa":true,"landing_page_url":"https://doi.org/10.60692/y1fs0-97s73","pdf_url":null,"source":{"id":"https://openalex.org/S7407051682","display_name":"Greater South Information System","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1016/j.rinp.2017.12.051","doi":"https://doi.org/10.1016/j.rinp.2017.12.051","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.rinp.2017.12.051","pdf_url":"https://www.sciencedirect.com/science/article/pii/S2211379717322003/pdf","source":{"id":"https://openalex.org/S2764941219","display_name":"Results in Physics","issn_l":"2211-3797","issn":["2211-3797"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","jufo-1","norway-1","poland-70"],"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Results in Physics","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2775976996.pdf","grobid_xml":"https://content.openalex.org/works/W2775976996.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W287497492","https://openalex.org/W1563165556","https://openalex.org/W1966553738","https://openalex.org/W1983326071","https://openalex.org/W1990934669","https://openalex.org/W1991832864","https://openalex.org/W1996615110","https://openalex.org/W2006852581","https://openalex.org/W2056780907","https://openalex.org/W2061980576","https://openalex.org/W2064354079","https://openalex.org/W2079776520","https://openalex.org/W2082698133","https://openalex.org/W2271858403","https://openalex.org/W2275336155","https://openalex.org/W2324048733","https://openalex.org/W2336711932","https://openalex.org/W2418871594","https://openalex.org/W2511698836","https://openalex.org/W2528180663","https://openalex.org/W2563188811","https://openalex.org/W2564733938","https://openalex.org/W2581978511","https://openalex.org/W2594303560","https://openalex.org/W2603894860","https://openalex.org/W2617574798","https://openalex.org/W2733810313","https://openalex.org/W2743205827","https://openalex.org/W2743467796","https://openalex.org/W2754389863","https://openalex.org/W2767353897","https://openalex.org/W2771267393","https://openalex.org/W3012873790","https://openalex.org/W6738432617"],"related_works":["https://openalex.org/W2792191619","https://openalex.org/W3158217983","https://openalex.org/W4248103533","https://openalex.org/W3046588275","https://openalex.org/W3085259849","https://openalex.org/W3046886605","https://openalex.org/W3049703542","https://openalex.org/W3008631921","https://openalex.org/W4313364931","https://openalex.org/W4302307873"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"constructed":[4],"a":[5],"travelling":[6],"wave":[7],"solution":[8],"for":[9,34],"space-time":[10,36,42],"fractional":[11,37,43,47],"nonlinear":[12,65],"partial":[13],"differential":[14,67],"equations":[15,63],"by":[16],"using":[17],"the":[18,35,51],"modified":[19,54],"extended":[20],"Tanh":[21],"method":[22,27],"with":[23],"Riccati":[24],"equation.":[25],"The":[26,46],"is":[28],"used":[29,59],"to":[30,60],"obtain":[31],"analytic":[32],"solutions":[33],"Klein-Gordon":[38],"and":[39,50],"coupled":[40],"conformable":[41],"Boussinesq":[44],"equations.":[45,68],"complex":[48],"transforms":[49],"properties":[52],"of":[53],"Riemann-Liouville":[55],"derivative":[56],"have":[57],"been":[58],"convert":[61],"these":[62],"into":[64],"ordinary":[66]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":17},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}