{"id":"https://openalex.org/W3042974430","doi":"https://doi.org/10.3390/sym12071195","title":"Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method","display_name":"Solution of Multi-Term Time-Fractional PDE Models Arising in Mathematical Biology and Physics by Local Meshless Method","publication_year":2020,"publication_date":"2020-07-19","ids":{"openalex":"https://openalex.org/W3042974430","doi":"https://doi.org/10.3390/sym12071195","mag":"3042974430"},"language":"en","primary_location":{"id":"doi:10.3390/sym12071195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071195","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1195/pdf?version=1595391728","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/7/1195/pdf?version=1595391728","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089160568","display_name":"Imtiaz Ahmad","orcid":"https://orcid.org/0000-0002-4023-3293"},"institutions":[{"id":"https://openalex.org/I4210142599","display_name":"University of Swabi","ror":"https://ror.org/04ez8az68","country_code":"PK","type":"education","lineage":["https://openalex.org/I4210142599"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Imtiaz Ahmad","raw_affiliation_strings":["Department of Mathematics, University of Swabi, Swabi 23430, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Swabi, Swabi 23430, Pakistan","institution_ids":["https://openalex.org/I4210142599"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114376646","display_name":"Hijaz Ahmad","orcid":"https://orcid.org/0000-0002-5438-5407"},"institutions":[{"id":"https://openalex.org/I90610274","display_name":"University of Engineering and Technology Peshawar","ror":"https://ror.org/00p034093","country_code":"PK","type":"education","lineage":["https://openalex.org/I90610274"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Hijaz Ahmad","raw_affiliation_strings":["Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan","institution_ids":["https://openalex.org/I90610274"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031839753","display_name":"Phatiphat Thounthong","orcid":null},"institutions":[{"id":"https://openalex.org/I82828225","display_name":"King Mongkut's University of Technology North Bangkok","ror":"https://ror.org/04fy6jb97","country_code":"TH","type":"education","lineage":["https://openalex.org/I82828225"]}],"countries":["TH"],"is_corresponding":false,"raw_author_name":"Phatiphat Thounthong","raw_affiliation_strings":["Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut\u2019s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand","Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand"],"affiliations":[{"raw_affiliation_string":"Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut\u2019s University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]},{"raw_affiliation_string":"Renewable Energy Research Centre, Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok, 1518 Pracharat 1 Road, Bangsue, Bangkok 10800, Thailand","institution_ids":["https://openalex.org/I82828225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046314241","display_name":"Yu\u2010Ming Chu","orcid":"https://orcid.org/0000-0002-0944-2134"},"institutions":[{"id":"https://openalex.org/I3018263800","display_name":"Huzhou University","ror":"https://ror.org/04mvpxy20","country_code":"CN","type":"education","lineage":["https://openalex.org/I3018263800"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yu-Ming Chu","raw_affiliation_strings":["Department of Mathematics, Huzhou University, Huzhou 313000, China","Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changasha, University of Science & Technology, Changsha 410114, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Huzhou University, Huzhou 313000, China","institution_ids":["https://openalex.org/I3018263800"]},{"raw_affiliation_string":"Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changasha, University of Science & Technology, Changsha 410114, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Roma, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5046314241"],"corresponding_institution_ids":["https://openalex.org/I3018263800"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.1513,"has_fulltext":true,"cited_by_count":113,"citation_normalized_percentile":{"value":0.94266424,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"12","issue":"7","first_page":"1195","last_page":"1195"},"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":0.9778000116348267,"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/T10514","display_name":"Numerical methods in engineering","score":0.9732000231742859,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8130328059196472},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.7124555706977844},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5798065662384033},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5695928931236267},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5393412709236145},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4980037212371826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46586087346076965},{"id":"https://openalex.org/keywords/regularized-meshless-method","display_name":"Regularized meshless method","score":0.45009028911590576},{"id":"https://openalex.org/keywords/symmetry","display_name":"Symmetry (geometry)","score":0.41692206263542175},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.41015467047691345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39608800411224365},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27207082509994507},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23943772912025452},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2043941617012024},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.17102372646331787},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07930803298950195}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8130328059196472},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.7124555706977844},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5798065662384033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5695928931236267},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5393412709236145},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4980037212371826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46586087346076965},{"id":"https://openalex.org/C177562122","wikidata":"https://www.wikidata.org/wiki/Q7309629","display_name":"Regularized meshless method","level":5,"score":0.45009028911590576},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.41692206263542175},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.41015467047691345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39608800411224365},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27207082509994507},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23943772912025452},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2043941617012024},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.17102372646331787},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07930803298950195},{"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},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"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/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym12071195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071195","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1195/pdf?version=1595391728","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:f047f796d28746e0ad2d6b243e675dd1","is_oa":true,"landing_page_url":"https://doaj.org/article/f047f796d28746e0ad2d6b243e675dd1","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 7, p 1195 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/7/1195/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12071195","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym12071195","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12071195","pdf_url":"https://www.mdpi.com/2073-8994/12/7/1195/pdf?version=1595391728","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1064001500","display_name":null,"funder_award_id":"61673169","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1503179675","display_name":null,"funder_award_id":"1971142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G171498429","display_name":null,"funder_award_id":"11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4499578435","display_name":null,"funder_award_id":"11701176, 11626101, 11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4844902455","display_name":null,"funder_award_id":"11626101","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4858060408","display_name":null,"funder_award_id":"11701176","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6016035139","display_name":null,"funder_award_id":"71202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6221780053","display_name":null,"funder_award_id":"11971","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6442795590","display_name":null,"funder_award_id":"11971142","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7346218018","display_name":null,"funder_award_id":"11871","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7739809515","display_name":null,"funder_award_id":"11871202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8460936770","display_name":null,"funder_award_id":"11971142, 11871202, 61673169, 11701176, 11626101, 11601485","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3042974430.pdf","grobid_xml":"https://content.openalex.org/works/W3042974430.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1991982189","https://openalex.org/W1992619775","https://openalex.org/W2083378485","https://openalex.org/W2134837756","https://openalex.org/W2147400514","https://openalex.org/W2165076033","https://openalex.org/W2254592078","https://openalex.org/W2312771969","https://openalex.org/W2524029403","https://openalex.org/W2607070827","https://openalex.org/W2611074852","https://openalex.org/W2620121926","https://openalex.org/W2766044013","https://openalex.org/W2776788713","https://openalex.org/W2782855242","https://openalex.org/W2898605082","https://openalex.org/W2904136109","https://openalex.org/W2910868904","https://openalex.org/W2911584126","https://openalex.org/W2914658081","https://openalex.org/W2914679279","https://openalex.org/W2922014217","https://openalex.org/W2973362193","https://openalex.org/W2974986442","https://openalex.org/W2981569003","https://openalex.org/W2990905930","https://openalex.org/W2994787573","https://openalex.org/W3021566603","https://openalex.org/W3034101448","https://openalex.org/W3038075946","https://openalex.org/W3040391847","https://openalex.org/W3043445804","https://openalex.org/W3046154426","https://openalex.org/W3081206333","https://openalex.org/W3093816455","https://openalex.org/W3121375162","https://openalex.org/W3122059167","https://openalex.org/W4230862244","https://openalex.org/W6648613085","https://openalex.org/W6758242905","https://openalex.org/W6771682714","https://openalex.org/W6812260443"],"related_works":["https://openalex.org/W2074635965","https://openalex.org/W3116192373","https://openalex.org/W32014465","https://openalex.org/W1521430315","https://openalex.org/W3150205597","https://openalex.org/W3185770440","https://openalex.org/W1627130620","https://openalex.org/W2313408818","https://openalex.org/W2211010819","https://openalex.org/W2066160882"],"abstract_inverted_index":{"Fractional":[0],"differential":[1],"equations":[2,32],"depict":[3],"nature":[4],"sufficiently":[5],"in":[6],"light":[7],"of":[8,26,43,94],"the":[9,23,44,49,55,61,89,95],"symmetry":[10],"properties":[11],"which":[12,87],"describe":[13],"biological":[14],"and":[15,78,83,92],"physical":[16],"processes.":[17],"This":[18],"article":[19],"is":[20,46,64],"concerned":[21],"with":[22],"numerical":[24,71],"treatment":[25],"three-term":[27],"time":[28],"fractional-order":[29],"multi-dimensional":[30],"diffusion":[31],"by":[33,48,66],"using":[34],"an":[35],"efficient":[36],"local":[37],"meshless":[38,51],"method.":[39,96],"The":[40,70],"space":[41],"derivative":[42],"models":[45],"discretized":[47,65],"proposed":[50],"procedure":[52],"based":[53],"on":[54,81],"multiquadric":[56],"radial":[57],"basis":[58],"function":[59],"though":[60],"time-fractional":[62],"part":[63],"Liouville\u2013Caputo":[67],"fractional":[68],"derivative.":[69],"results":[72],"are":[73],"obtained":[74],"for":[75],"one-,":[76],"two-":[77],"three-dimensional":[79],"cases":[80],"rectangular":[82],"non-rectangular":[84],"computational":[85],"domains":[86],"verify":[88],"validity,":[90],"efficiency":[91],"accuracy":[93]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":21},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":27},{"year":2020,"cited_by_count":21}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}