{"id":"https://openalex.org/W1973830572","doi":"https://doi.org/10.1155/2013/482419","title":"Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations","display_name":"Numerical Solutions for the Time and Space Fractional Nonlinear Partial Differential Equations","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W1973830572","doi":"https://doi.org/10.1155/2013/482419","mag":"1973830572"},"language":"en","primary_location":{"id":"doi:10.1155/2013/482419","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/482419","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/482419.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","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/jam/2013/482419.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010614092","display_name":"Khaled A. Gepreel","orcid":"https://orcid.org/0000-0001-5542-8694"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]},{"id":"https://openalex.org/I192398990","display_name":"Zagazig University","ror":"https://ror.org/053g6we49","country_code":"EG","type":"education","lineage":["https://openalex.org/I192398990"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Khaled A. Gepreel","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt","Mathematics Department, Faculty of Science, Taif University, Taif","Mathematics Department, Faculty of Science, Zagazig University, Zagazig"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt","institution_ids":["https://openalex.org/I192398990"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif","institution_ids":["https://openalex.org/I179331831"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Zagazig University, Zagazig","institution_ids":["https://openalex.org/I192398990"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076063109","display_name":"Taher A. Nofal","orcid":"https://orcid.org/0000-0002-4243-9594"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]},{"id":"https://openalex.org/I89466785","display_name":"Minia University","ror":"https://ror.org/02hcv4z63","country_code":"EG","type":"education","lineage":["https://openalex.org/I89466785"]}],"countries":["EG","SA"],"is_corresponding":false,"raw_author_name":"Taher A. Nofal","raw_affiliation_strings":["Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt","Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","Mathematics Department, Faculty  of Science, El-Minia University, El-Minia","Mathematics Department, Faculty of Science, Taif University, Taif"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, El-Minia University, El-Minia, Egypt","institution_ids":["https://openalex.org/I89466785"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]},{"raw_affiliation_string":"Mathematics Department, Faculty  of Science, El-Minia University, El-Minia","institution_ids":["https://openalex.org/I89466785"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif","institution_ids":["https://openalex.org/I179331831"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011208576","display_name":"Fawziah M. Alotaibi","orcid":"https://orcid.org/0000-0002-7173-5237"},"institutions":[{"id":"https://openalex.org/I179331831","display_name":"Taif University","ror":"https://ror.org/014g1a453","country_code":"SA","type":"education","lineage":["https://openalex.org/I179331831"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Fawziah M. Alotaibi","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","Mathematics Department, Faculty of Science, Taif University, Taif"],"raw_orcid":"https://orcid.org/0000-0002-7173-5237","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif, Saudi Arabia","institution_ids":["https://openalex.org/I179331831"]},{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Taif University, Taif","institution_ids":["https://openalex.org/I179331831"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010614092"],"corresponding_institution_ids":["https://openalex.org/I179331831","https://openalex.org/I192398990"],"apc_list":{"value":1025,"currency":"USD","value_usd":1025},"apc_paid":{"value":1025,"currency":"USD","value_usd":1025},"fwci":0.8112,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69829153,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"12"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9994999766349792,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.7840094566345215},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.640570878982544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5505238175392151},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5090388655662537},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4644472897052765},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4367442727088928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3922472596168518},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3457004427909851},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12169063091278076}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7840094566345215},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.640570878982544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5505238175392151},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5090388655662537},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4644472897052765},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4367442727088928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3922472596168518},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3457004427909851},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12169063091278076},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1155/2013/482419","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/482419","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/482419.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1394808228","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1394808228","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:RePEc:hin:jnljam:482419","is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/JAM/2013/482419.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:9730aaccdd3c4a999e15e7482db7593c","is_oa":true,"landing_page_url":"https://doaj.org/article/9730aaccdd3c4a999e15e7482db7593c","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":"Journal of Applied Mathematics, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/482419","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/482419","pdf_url":"https://downloads.hindawi.com/journals/jam/2013/482419.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"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":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1973830572.pdf","grobid_xml":"https://content.openalex.org/works/W1973830572.grobid-xml"},"referenced_works_count":43,"referenced_works":["https://openalex.org/W1500387703","https://openalex.org/W1809943628","https://openalex.org/W1966324062","https://openalex.org/W1966553738","https://openalex.org/W1970467391","https://openalex.org/W1974932120","https://openalex.org/W1977718189","https://openalex.org/W1983396466","https://openalex.org/W1994034594","https://openalex.org/W1994821936","https://openalex.org/W1995487946","https://openalex.org/W1997858083","https://openalex.org/W2002138473","https://openalex.org/W2006956631","https://openalex.org/W2008152104","https://openalex.org/W2018027770","https://openalex.org/W2018836488","https://openalex.org/W2034424151","https://openalex.org/W2043086833","https://openalex.org/W2052590815","https://openalex.org/W2053833421","https://openalex.org/W2056456131","https://openalex.org/W2061488318","https://openalex.org/W2069729301","https://openalex.org/W2078564620","https://openalex.org/W2080816188","https://openalex.org/W2081261686","https://openalex.org/W2086396968","https://openalex.org/W2089608075","https://openalex.org/W2091662017","https://openalex.org/W2098940483","https://openalex.org/W2131079340","https://openalex.org/W2141858378","https://openalex.org/W2146423481","https://openalex.org/W2166550727","https://openalex.org/W2183087555","https://openalex.org/W2290477736","https://openalex.org/W2313292381","https://openalex.org/W2314590580","https://openalex.org/W2324422198","https://openalex.org/W3102894372","https://openalex.org/W4231069456","https://openalex.org/W4240465921"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W4246784705","https://openalex.org/W2253351617","https://openalex.org/W2065284654","https://openalex.org/W3121927021","https://openalex.org/W2999616507","https://openalex.org/W2118964038","https://openalex.org/W2748563398","https://openalex.org/W2043671984"],"abstract_inverted_index":{"We":[0,58,98],"implement":[1],"relatively":[2],"analytical":[3],"techniques,":[4],"the":[5,15,32,44,49,61,71,76,82,100],"homotopy":[6],"perturbation":[7],"method,":[8],"and":[9,20],"variational":[10],"iteration":[11],"method":[12,105],"to":[13,42,73,86,93,106],"find":[14,107],"approximate":[16,46,62,77],"solutions":[17,47,63,109],"for":[18,48],"time":[19],"space":[21],"fractional":[22,27,55,83,90,112],"Benjamin-Bona":[23],"Mahony":[24],"equation.":[25,57,114],"The":[26],"derivatives":[28],"are":[29,37],"described":[30],"in":[31,39],"Caputo":[33],"sense.":[34],"These":[35],"methods":[36],"used":[38],"applied":[40],"mathematics":[41],"obtain":[43],"analytic":[45],"nonlinear":[50,88,94,111],"Bejamin-Bona":[51],"Mahoney":[52],"(BBM)":[53],"partial":[54,89],"differential":[56,91,96],"compare":[59,74],"between":[60,75],"obtained":[64],"by":[65],"these":[66],"methods.":[67],"Also,":[68,79],"we":[69,80],"present":[70],"figures":[72],"solutions.":[78],"use":[81,99],"complex":[84],"transformation":[85],"convert":[87],"equations":[92],"ordinary":[95],"equations.":[97],"improved":[101],"(":[102],"/)-expansion":[103],"function":[104],"exact":[108],"of":[110],"BBM":[113]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2014,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}