{"id":"https://openalex.org/W4411978804","doi":"https://doi.org/10.3390/axioms14070515","title":"Hexic-Chebyshev Collocation Method for Solving Distributed-Order Time-Space Fractional Diffusion Equations","display_name":"Hexic-Chebyshev Collocation Method for Solving Distributed-Order Time-Space Fractional Diffusion Equations","publication_year":2025,"publication_date":"2025-07-03","ids":{"openalex":"https://openalex.org/W4411978804","doi":"https://doi.org/10.3390/axioms14070515"},"language":"en","primary_location":{"id":"doi:10.3390/axioms14070515","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070515","pdf_url":null,"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://doi.org/10.3390/axioms14070515","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019248671","display_name":"Afshin Babaei","orcid":"https://orcid.org/0000-0002-6980-9786"},"institutions":[{"id":"https://openalex.org/I4871159","display_name":"University of Mazandaran","ror":"https://ror.org/05fp9g671","country_code":"IR","type":"education","lineage":["https://openalex.org/I4871159"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"Afshin Babaei","raw_affiliation_strings":["Department of Applied Mathematics, University of Mazandaran, Babolsar 47415-95477, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Mazandaran, Babolsar 47415-95477, Iran","institution_ids":["https://openalex.org/I4871159"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073564977","display_name":"Seddigheh Banihashemi","orcid":"https://orcid.org/0000-0002-4449-8109"},"institutions":[{"id":"https://openalex.org/I4871159","display_name":"University of Mazandaran","ror":"https://ror.org/05fp9g671","country_code":"IR","type":"education","lineage":["https://openalex.org/I4871159"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Sedigheh Banihashemi","raw_affiliation_strings":["Department of Applied Mathematics, University of Mazandaran, Babolsar 47415-95477, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Mazandaran, Babolsar 47415-95477, Iran","institution_ids":["https://openalex.org/I4871159"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077062428","display_name":"Behrouz Parsa Moghaddam","orcid":"https://orcid.org/0000-0003-4957-9028"},"institutions":[{"id":"https://openalex.org/I33162209","display_name":"Islamic Azad University, Lahijan Branch","ror":"https://ror.org/03dhqyc75","country_code":"IR","type":"education","lineage":["https://openalex.org/I110525433","https://openalex.org/I33162209"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"Behrouz Parsa Moghaddam","raw_affiliation_strings":["Department of Mathematics, La.C., Islamic Azad University, Lahijan 44169-39515, Iran"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, La.C., Islamic Azad University, Lahijan 44169-39515, Iran","institution_ids":["https://openalex.org/I33162209"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045607543","display_name":"Arman Dabiri","orcid":"https://orcid.org/0000-0002-4407-4314"},"institutions":[{"id":"https://openalex.org/I138006243","display_name":"University of Arizona","ror":"https://ror.org/03m2x1q45","country_code":"US","type":"education","lineage":["https://openalex.org/I138006243"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arman Dabiri","raw_affiliation_strings":["Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA"],"affiliations":[{"raw_affiliation_string":"Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA","institution_ids":["https://openalex.org/I138006243"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5019248671"],"corresponding_institution_ids":["https://openalex.org/I4871159"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.4683,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.817427,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"14","issue":"7","first_page":"515","last_page":"515"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9954000115394592,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.994700014591217,"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/chebyshev-filter","display_name":"Chebyshev filter","score":0.653721034526825},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6212050318717957},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6042529344558716},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5851604342460632},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5497182607650757},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5438060164451599},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5242293477058411},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.5154555439949036},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4846137464046478},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4510681629180908},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43592193722724915},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25066518783569336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15355336666107178},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08536714315414429}],"concepts":[{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.653721034526825},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6212050318717957},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6042529344558716},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5851604342460632},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5497182607650757},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5438060164451599},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5242293477058411},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.5154555439949036},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4846137464046478},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4510681629180908},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43592193722724915},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25066518783569336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15355336666107178},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08536714315414429},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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":2,"locations":[{"id":"doi:10.3390/axioms14070515","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070515","pdf_url":null,"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:303adb8f55094ce1addbae57db1787b6","is_oa":true,"landing_page_url":"https://doaj.org/article/303adb8f55094ce1addbae57db1787b6","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 14, Iss 7, p 515 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/axioms14070515","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms14070515","pdf_url":null,"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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":69,"referenced_works":["https://openalex.org/W104068007","https://openalex.org/W1571391776","https://openalex.org/W1577190993","https://openalex.org/W1655132380","https://openalex.org/W1975900429","https://openalex.org/W2006281429","https://openalex.org/W2007553558","https://openalex.org/W2011394976","https://openalex.org/W2017663693","https://openalex.org/W2026946703","https://openalex.org/W2040329976","https://openalex.org/W2088338349","https://openalex.org/W2090239694","https://openalex.org/W2110245394","https://openalex.org/W2111271983","https://openalex.org/W2128614559","https://openalex.org/W2137120557","https://openalex.org/W2137696066","https://openalex.org/W2146447064","https://openalex.org/W2163467777","https://openalex.org/W2182721444","https://openalex.org/W2251960872","https://openalex.org/W2466433738","https://openalex.org/W2545607144","https://openalex.org/W2591074847","https://openalex.org/W2594658257","https://openalex.org/W2601895526","https://openalex.org/W2605896013","https://openalex.org/W2606385482","https://openalex.org/W2738935813","https://openalex.org/W2774959299","https://openalex.org/W2782302440","https://openalex.org/W2789789392","https://openalex.org/W2794751236","https://openalex.org/W2800683077","https://openalex.org/W2807725388","https://openalex.org/W2883589886","https://openalex.org/W2898274868","https://openalex.org/W2902797372","https://openalex.org/W2913984069","https://openalex.org/W2925828089","https://openalex.org/W2947825288","https://openalex.org/W2948851489","https://openalex.org/W2962879816","https://openalex.org/W2963805080","https://openalex.org/W2970494462","https://openalex.org/W2990630441","https://openalex.org/W3014569360","https://openalex.org/W3029070471","https://openalex.org/W3032584751","https://openalex.org/W3047033524","https://openalex.org/W3047531212","https://openalex.org/W3047637034","https://openalex.org/W3118822988","https://openalex.org/W3186077100","https://openalex.org/W4200005720","https://openalex.org/W4241819982","https://openalex.org/W4324295726","https://openalex.org/W4394694425","https://openalex.org/W4396674678","https://openalex.org/W4408946206","https://openalex.org/W4409075035","https://openalex.org/W6604274123","https://openalex.org/W6676170769","https://openalex.org/W6680069083","https://openalex.org/W6685764665","https://openalex.org/W6719786346","https://openalex.org/W6760542532","https://openalex.org/W6763231262"],"related_works":["https://openalex.org/W2078318892","https://openalex.org/W2791210196","https://openalex.org/W1987365920","https://openalex.org/W322101810","https://openalex.org/W2382532955","https://openalex.org/W2106962382","https://openalex.org/W2384941625","https://openalex.org/W2541927208","https://openalex.org/W1989122168","https://openalex.org/W2009058751"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,64],"spectral":[4],"method":[5,57],"to":[6,23,27,58,91,111,124],"solve":[7,24],"nonlinear":[8,67],"distributed-order":[9,35],"diffusion":[10],"equations":[11],"with":[12,119,148],"both":[13],"time-distributed-order":[14],"and":[15,32,40,100,155],"two-sided":[16],"space-fractional":[17],"terms.":[18],"These":[19],"are":[20,50,146],"highly":[21],"challenging":[22],"analytically":[25],"due":[26,90],"the":[28,33,38,53,56,60,80,113,116,129,143,152],"interplay":[29],"between":[30],"nonlinearity":[31],"fractional":[34],"nature":[36],"of":[37,55,66,86,115],"time":[39],"space":[41],"derivatives.":[42],"For":[43],"this":[44],"purpose,":[45],"Hexic-kind":[46],"Chebyshev":[47],"polynomials":[48],"(HCPs)":[49],"used":[51],"as":[52,79],"backbone":[54],"transform":[59],"primary":[61,84],"problem":[62],"into":[63],"set":[65],"algebraic":[68],"equations,":[69],"which":[70],"can":[71],"be":[72],"efficiently":[73],"solved":[74],"using":[75],"numerical":[76,144],"solvers,":[77],"such":[78],"Newton\u2013Raphson":[81],"method.":[82],"The":[83,132],"reason":[85],"choosing":[87],"HCPs":[88],"is":[89,135],"their":[92,97],"remarkable":[93],"recurrence":[94],"relations,":[95],"facilitating":[96],"efficient":[98],"computation":[99],"manipulation":[101],"in":[102],"mathematical":[103],"analyses.":[104],"A":[105],"comprehensive":[106],"convergence":[107],"analysis":[108],"was":[109],"conducted":[110],"validate":[112],"robustness":[114],"proposed":[117],"method,":[118],"an":[120],"error":[121],"bound":[122],"derived":[123],"provide":[125],"theoretical":[126],"guarantees":[127],"for":[128],"solution\u2019s":[130],"accuracy.":[131],"method\u2019s":[133],"effectiveness":[134],"further":[136],"demonstrated":[137],"through":[138],"two":[139],"test":[140],"examples,":[141],"where":[142],"results":[145],"compared":[147],"existing":[149],"solutions,":[150],"confirming":[151],"approach\u2019s":[153],"accuracy":[154],"reliability.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-13T16:22:10.518609","created_date":"2025-10-10T00:00:00"}
