{"id":"https://openalex.org/W4413131408","doi":"https://doi.org/10.3390/axioms14080617","title":"Modulation Instability and Abundant Exact Solitons to the Fractional Mathematical Physics Model Through Two Distinct Methods","display_name":"Modulation Instability and Abundant Exact Solitons to the Fractional Mathematical Physics Model Through Two Distinct Methods","publication_year":2025,"publication_date":"2025-08-08","ids":{"openalex":"https://openalex.org/W4413131408","doi":"https://doi.org/10.3390/axioms14080617"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14080617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080617","pdf_url":"https://www.mdpi.com/2075-1680/14/8/617/pdf?version=1754635908","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/14/8/617/pdf?version=1754635908","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010728851","display_name":"Abdulaziz Khalid Alsharidi","orcid":"https://orcid.org/0009-0007-2527-7398"},"institutions":[{"id":"https://openalex.org/I4626487","display_name":"King Faisal University","ror":"https://ror.org/00dn43547","country_code":"SA","type":"education","lineage":["https://openalex.org/I4626487"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Abdulaziz Khalid Alsharidi","raw_affiliation_strings":["Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Hasa 31982, Saudi Arabia","institution_ids":["https://openalex.org/I4626487"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042426376","display_name":"Ahmet Bekir","orcid":"https://orcid.org/0000-0001-9394-4681"},"institutions":[{"id":"https://openalex.org/I4210091745","display_name":"Eski\u015fehir City Hospital","ror":"https://ror.org/00czdkn85","country_code":"TR","type":"healthcare","lineage":["https://openalex.org/I1303077703","https://openalex.org/I4210091745"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Ahmet Bekir","raw_affiliation_strings":["Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030 Eskisehir, Turkey"],"raw_orcid":"https://orcid.org/0000-0001-9394-4681","affiliations":[{"raw_affiliation_string":"Neighbourhood of Akcaglan, Imarli Street, Number: 28/4, 26030 Eskisehir, Turkey","institution_ids":["https://openalex.org/I4210091745"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5042426376"],"corresponding_institution_ids":["https://openalex.org/I4210091745"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21823383,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"8","first_page":"617","last_page":"617"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.982699990272522,"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/soliton","display_name":"Soliton","score":0.6391280889511108},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.6304029822349548},{"id":"https://openalex.org/keywords/instability","display_name":"Instability","score":0.607041597366333},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5878578424453735},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.5137492418289185},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5061506628990173},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4732414186000824},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46601206064224243},{"id":"https://openalex.org/keywords/modulation","display_name":"Modulation (music)","score":0.46546411514282227},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.43584102392196655},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.42971307039260864},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.42259469628334045},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.34516650438308716},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.3347797095775604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3310760259628296},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2591727077960968},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22491100430488586},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.16744256019592285},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.12578025460243225}],"concepts":[{"id":"https://openalex.org/C87651913","wikidata":"https://www.wikidata.org/wiki/Q464949","display_name":"Soliton","level":3,"score":0.6391280889511108},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.6304029822349548},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.607041597366333},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5878578424453735},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.5137492418289185},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5061506628990173},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4732414186000824},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46601206064224243},{"id":"https://openalex.org/C123079801","wikidata":"https://www.wikidata.org/wiki/Q750240","display_name":"Modulation (music)","level":2,"score":0.46546411514282227},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.43584102392196655},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.42971307039260864},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.42259469628334045},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.34516650438308716},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.3347797095775604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3310760259628296},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2591727077960968},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22491100430488586},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.16744256019592285},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.12578025460243225},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/axioms14080617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080617","pdf_url":"https://www.mdpi.com/2075-1680/14/8/617/pdf?version=1754635908","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:00daa155f72a4f2aa79c166514e2062a","is_oa":true,"landing_page_url":"https://doaj.org/article/00daa155f72a4f2aa79c166514e2062a","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":"Axioms, Vol 14, Iss 8, p 617 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14080617","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14080617","pdf_url":"https://www.mdpi.com/2075-1680/14/8/617/pdf?version=1754635908","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320331156","display_name":"King Faisal University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4413131408.pdf","grobid_xml":"https://content.openalex.org/works/W4413131408.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W2051495326","https://openalex.org/W2744262367","https://openalex.org/W2773541801","https://openalex.org/W2913927477","https://openalex.org/W2963520255","https://openalex.org/W3024272477","https://openalex.org/W3035278315","https://openalex.org/W3096331784","https://openalex.org/W3209779712","https://openalex.org/W4200555509","https://openalex.org/W4224250381","https://openalex.org/W4281765473","https://openalex.org/W4309009990","https://openalex.org/W4313503220","https://openalex.org/W4319242253","https://openalex.org/W4378648159","https://openalex.org/W4378760183","https://openalex.org/W4386329197","https://openalex.org/W4387342892","https://openalex.org/W4393855568","https://openalex.org/W4397290339","https://openalex.org/W4400574430","https://openalex.org/W4401334831","https://openalex.org/W4402270345","https://openalex.org/W4405847686","https://openalex.org/W4405947326","https://openalex.org/W4407230819","https://openalex.org/W4407597184","https://openalex.org/W4408473038","https://openalex.org/W4409269052","https://openalex.org/W6663169203","https://openalex.org/W6844433889"],"related_works":["https://openalex.org/W2615167981","https://openalex.org/W2037143908","https://openalex.org/W2782555567","https://openalex.org/W4243325204","https://openalex.org/W72566090","https://openalex.org/W3150371131","https://openalex.org/W2387283721","https://openalex.org/W4281631492","https://openalex.org/W2077597484","https://openalex.org/W2758674499"],"abstract_inverted_index":{"The":[0,67,83,95,158],"paper":[1],"consists":[2],"of":[3,6,46,64,74,79,114],"various":[4,90],"types":[5],"wave":[7],"solutions":[8,73,108,116],"for":[9],"the":[10,23,44,47,52,71,75,80,106,115,125,139,146,156],"truncated":[11],"M-fractional":[12],"Bateman\u2013Burgers":[13,76],"equation,":[14],"a":[15,131],"significant":[16],"mathematical":[17],"physics":[18],"equation.":[19],"This":[20],"model":[21,77,126],"describes":[22],"nonlinear":[24],"waves":[25],"and":[26,51,92,104,109,119,150,163],"solitons":[27],"in":[28,89,102,117,127,148],"different":[29],"physical":[30],"fields":[31],"such":[32],"as":[33],"optical":[34],"fibers,":[35],"plasma":[36],"physics,":[37],"fluid":[38],"dynamics,":[39],"traffic":[40],"flow,":[41],"etc.":[42],"Through":[43],"application":[45],"expa":[48],"function":[49],"method":[50],"modified":[53],"simplest":[54],"equation":[55],"method,":[56],"we":[57],"are":[58,161],"able":[59],"to":[60,100,110],"obtain":[61,111],"exact":[62,107],"series":[63],"soliton":[65],"solutions.":[66],"results":[68,85],"differ":[69],"from":[70,155],"current":[72],"because":[78],"fractional":[81],"derivative.":[82],"achieved":[84],"could":[86],"be":[87],"helpful":[88],"engineering":[91],"scientific":[93],"domains.":[94],"Mathematica":[96],"software":[97],"is":[98,129,134],"used":[99,160],"assist":[101],"obtaining":[103],"verifying":[105],"contour":[112],"plots":[113],"two":[118],"three":[120],"dimensions.":[121],"To":[122],"ensure":[123],"that":[124],"question":[128,149],"stable,":[130],"stability":[132],"analysis":[133],"also":[135],"carried":[136],"out":[137],"using":[138],"modulation":[140],"instability":[141],"method.":[142],"Future":[143],"research":[144],"on":[145],"system":[147],"related":[151],"systems":[152],"will":[153],"benefit":[154],"findings.":[157],"methods":[159],"simple":[162],"effective.":[164]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}