{"id":"https://openalex.org/W2754127966","doi":"https://doi.org/10.1515/cmam-2017-0035","title":"A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions","display_name":"A Time-Fractional Diffusion Equation with Generalized Memory Kernel in Differential and Difference Settings with Smooth Solutions","publication_year":2017,"publication_date":"2017-09-09","ids":{"openalex":"https://openalex.org/W2754127966","doi":"https://doi.org/10.1515/cmam-2017-0035","mag":"2754127966"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2017-0035","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0035","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047265134","display_name":"Anatoly A. Alikhanov","orcid":"https://orcid.org/0000-0003-0684-6667"},"institutions":[{"id":"https://openalex.org/I4210093841","display_name":"Institute of Applied Mathematics","ror":"https://ror.org/00h9jx107","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I1313323035","https://openalex.org/I4210093841","https://openalex.org/I4210124601","https://openalex.org/I4210148470"]},{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Anatoly A. Alikhanov","raw_affiliation_strings":["Institute of Applied Mathematics and Automation KBSC RAS , ul. Shortanova 89 A , Nalchik , 360000 , Russia"],"raw_orcid":"https://orcid.org/0000-0003-0684-6667","affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics and Automation KBSC RAS , ul. Shortanova 89 A , Nalchik , 360000 , Russia","institution_ids":["https://openalex.org/I4210105350","https://openalex.org/I4210093841"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5047265134"],"corresponding_institution_ids":["https://openalex.org/I4210093841","https://openalex.org/I4210105350"],"apc_list":null,"apc_paid":null,"fwci":0.8045,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.71730769,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"17","issue":"4","first_page":"647","last_page":"660"},"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":0.9994000196456909,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9976999759674072,"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":0.759143590927124},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5561062693595886},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5122970342636108},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.4965677857398987},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.45540982484817505},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37891459465026855},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3516967296600342},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3211125135421753}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.759143590927124},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5561062693595886},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5122970342636108},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.4965677857398987},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.45540982484817505},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37891459465026855},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3516967296600342},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3211125135421753},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2017-0035","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2017-0035","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8500000238418579}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1510837990","https://openalex.org/W1976424989","https://openalex.org/W2038588805","https://openalex.org/W2041540906","https://openalex.org/W2044695655","https://openalex.org/W2047594597","https://openalex.org/W2062266804","https://openalex.org/W2065232540","https://openalex.org/W2092440717","https://openalex.org/W2120075729","https://openalex.org/W2345649492","https://openalex.org/W2394699789","https://openalex.org/W2510459129","https://openalex.org/W2608656286","https://openalex.org/W2963020731","https://openalex.org/W2964083141","https://openalex.org/W2964248750","https://openalex.org/W3102362377","https://openalex.org/W4205604664","https://openalex.org/W4301223505"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W2980963558","https://openalex.org/W2253351617","https://openalex.org/W2065284654","https://openalex.org/W3121927021","https://openalex.org/W3215562268","https://openalex.org/W2021368388","https://openalex.org/W2000813003","https://openalex.org/W2930126963"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,43],"paper,":[3],"an":[4],"a":[5,25],"priori":[6],"estimate":[7],"for":[8,84,139],"the":[9,17,20,29,58,66,85,97,105,117,121,124],"corresponding":[10],"differential":[11],"problem":[12],"is":[13],"obtained":[14,130],"by":[15,134],"using":[16],"method":[18],"of":[19,28,42,57,96,123],"energy":[21],"inequalities.":[22],"We":[23],"construct":[24],"difference":[26,44,53],"analog":[27],"Caputo":[30],"fractional":[31],"derivative":[32],"with":[33,90,116],"generalized":[34,86],"memory":[35],"kernel":[36],"(L1":[37],"formula).":[38],"The":[39,129],"basic":[40],"properties":[41],"operator":[45],"are":[46,93,127,132],"investigated":[47],"and":[48,60,65,100],"on":[49],"its":[50],"basis":[51],"some":[52,140],"schemes":[54,99],"generating":[55],"approximations":[56],"second":[59],"fourth":[61],"order":[62,81,122],"in":[63,82,104],"space":[64],"<m:math":[67,107],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[68,108],"<m:mrow>":[69,71],"<m:mo>(</m:mo>":[70],"<m:mn>2</m:mn>":[72,111],"<m:mo>-</m:mo>":[73],"<m:mi>\u03b1</m:mi>":[74],"</m:mrow>":[75,77],"<m:mo>)</m:mo>":[76],"</m:math>":[78,113],"{(2-\\alpha)}":[79],"-th":[80],"time":[83],"time-fractional":[87],"diffusion":[88],"equation":[89],"variable":[91],"coefficients":[92],"considered.":[94],"Stability":[95],"suggested":[98],"also":[101],"their":[102],"convergence":[103],"grid":[106],"<m:msub>":[109],"<m:mi>L</m:mi>":[110],"</m:msub>":[112],"{L_{2}}":[114],"-norm":[115],"rate":[118],"equal":[119],"to":[120],"approximation":[125],"error":[126],"proved.":[128],"results":[131],"supported":[133],"numerical":[135],"calculations":[136],"carried":[137],"out":[138],"test":[141],"problems.":[142]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1}],"updated_date":"2026-05-10T08:33:47.465468","created_date":"2025-10-10T00:00:00"}