{"id":"https://openalex.org/W4406778369","doi":"https://doi.org/10.1007/s12190-025-02371-w","title":"Chebyshev Petrov\u2013Galerkin method for nonlinear time-fractional integro-differential equations with a mildly singular kernel","display_name":"Chebyshev Petrov\u2013Galerkin method for nonlinear time-fractional integro-differential equations with a mildly singular kernel","publication_year":2025,"publication_date":"2025-01-23","ids":{"openalex":"https://openalex.org/W4406778369","doi":"https://doi.org/10.1007/s12190-025-02371-w"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-025-02371-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-025-02371-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-025-02371-w.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"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":"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 and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s12190-025-02371-w.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052038000","display_name":"Y. H. Youssri","orcid":"https://orcid.org/0000-0003-0403-8797"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]}],"countries":["EG"],"is_corresponding":true,"raw_author_name":"Y. H. Youssri","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-0403-8797","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5006833725","display_name":"Ahmed Gamal Atta","orcid":"https://orcid.org/0000-0003-1467-640X"},"institutions":[{"id":"https://openalex.org/I107720978","display_name":"Ain Shams University","ror":"https://ror.org/00cb9w016","country_code":"EG","type":"education","lineage":["https://openalex.org/I107720978"]}],"countries":["EG"],"is_corresponding":false,"raw_author_name":"A. G. Atta","raw_affiliation_strings":["Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, 11341, Egypt"],"raw_orcid":"https://orcid.org/0000-0003-1467-640X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, 11341, Egypt","institution_ids":["https://openalex.org/I107720978"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052038000"],"corresponding_institution_ids":["https://openalex.org/I145487455"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":23.2575,"has_fulltext":true,"cited_by_count":21,"citation_normalized_percentile":{"value":0.99787764,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"71","issue":"3","first_page":"3891","last_page":"3911"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9980999827384949,"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/mathematics","display_name":"Mathematics","score":0.8355894088745117},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6483334898948669},{"id":"https://openalex.org/keywords/petrov\u2013galerkin-method","display_name":"Petrov\u2013Galerkin method","score":0.6440425515174866},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6135728359222412},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.6125867366790771},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5944262146949768},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5692136287689209},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5204768180847168},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5008907318115234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49294376373291016},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15396970510482788},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11969864368438721},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.08143094182014465},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06070801615715027}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8355894088745117},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6483334898948669},{"id":"https://openalex.org/C2778540877","wikidata":"https://www.wikidata.org/wiki/Q7179155","display_name":"Petrov\u2013Galerkin method","level":3,"score":0.6440425515174866},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6135728359222412},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.6125867366790771},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5944262146949768},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5692136287689209},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5204768180847168},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5008907318115234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49294376373291016},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15396970510482788},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11969864368438721},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.08143094182014465},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06070801615715027},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-025-02371-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-025-02371-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-025-02371-w.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"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":"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 and Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s12190-025-02371-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s12190-025-02371-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s12190-025-02371-w.pdf","source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"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":"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 and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321148","display_name":"Cairo University","ror":"https://ror.org/03q21mh05"},{"id":"https://openalex.org/F4320321655","display_name":"Science and Technology Development Fund","ror":"https://ror.org/044vr6g03"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4406778369.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W2089783545","https://openalex.org/W2259227674","https://openalex.org/W2541035753","https://openalex.org/W2804199700","https://openalex.org/W3081671812","https://openalex.org/W3166463534","https://openalex.org/W3183392843","https://openalex.org/W3187578234","https://openalex.org/W4236569700","https://openalex.org/W4254246953","https://openalex.org/W4307262692","https://openalex.org/W4308426653","https://openalex.org/W4313145648","https://openalex.org/W4313889479","https://openalex.org/W4319313319","https://openalex.org/W4322500839","https://openalex.org/W4323539435","https://openalex.org/W4323840376","https://openalex.org/W4372317553","https://openalex.org/W4377137199","https://openalex.org/W4378190659","https://openalex.org/W4386101211","https://openalex.org/W4388015499","https://openalex.org/W4388339828","https://openalex.org/W4389940056","https://openalex.org/W4390929092","https://openalex.org/W4404417961"],"related_works":["https://openalex.org/W4288262055","https://openalex.org/W2967076701","https://openalex.org/W2990320605","https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W2541927208","https://openalex.org/W4213342932","https://openalex.org/W2056379897","https://openalex.org/W2410898212","https://openalex.org/W3136108301"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,147],"paper,":[3],"a":[4,25,48,83,108,161],"new":[5],"approach":[6,116],"to":[7,101,107,164],"time-fractional":[8],"partial":[9,154],"integro-differential":[10,155],"equations":[11,72],"with":[12,139],"weakly":[13],"singular":[14],"kernels":[15],"(":[16,35],"TFPIDE":[17],")":[18,37],"is":[19],"presented.":[20],"The":[21,57,104,142],"suggested":[22,134],"method":[23,148],"produces":[24],"spectral":[26],"semi-analytic":[27],"solution":[28],"by":[29,97,117,137],"using":[30,64],"shifted":[31],"first-kind":[32],"Chebyshev":[33],"polynomials":[34],"SCP1K":[36],"as":[38,160],"basis":[39,52],"functions.":[40],"To":[41],"satisfy":[42],"homogeneous":[43],"beginning":[44],"and":[45,91,121,130],"boundary":[46],"requirements,":[47],"suitable":[49],"collection":[50],"of":[51,75,111,114,132,167],"functions":[53],"should":[54],"be":[55,102],"chosen.":[56],"unknown":[58],"expansion":[59],"coefficients":[60],"are":[61],"then":[62],"found":[63],"the":[65,76,88,93,98,112,115,127,133,165,170],"Petrov\u2013Galerkin":[66,99],"technique.":[67],"Interestingly,":[68],"we":[69],"obtain":[70],"precise":[71],"for":[73,150],"each":[74],"related":[77],"matrices\u2019":[78],"elements.":[79],"These":[80],"matrices":[81],"follow":[82],"clear":[84],"pattern":[85],"that":[86],"facilitates":[87],"inversion":[89],"procedure":[90],"allows":[92],"algebraic":[94],"problem":[95],"generated":[96],"technique":[100],"solved.":[103],"work":[105],"contributes":[106],"better":[109],"knowledge":[110,168],"dependability":[113],"thoroughly":[118],"examining":[119],"convergence":[120],"error":[122],"analysis.":[123],"Numerical":[124],"examples":[125],"demonstrate":[126,144],"applicability,":[128],"accuracy,":[129],"efficiency":[131],"technique,":[135],"supplemented":[136],"comparisons":[138],"previous":[140],"research.":[141],"outcomes":[143],"how":[145],"well":[146],"works":[149],"solving":[151],"time":[152],"fractional":[153],"equations,":[156],"highlighting":[157],"its":[158],"importance":[159],"useful":[162],"contribution":[163],"body":[166],"in":[169],"area.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":16}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}