{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T01:05:41Z","timestamp":1728176741556},"reference-count":46,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T00:00:00Z","timestamp":1604448000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2021,3]]},"abstract":"Abstract<\/jats:title>In this article, we study the numerical technique for variable\u2010order fractional reaction\u2010diffusion and subdiffusion equations that the fractional derivative is described in Caputo's sense. The discrete scheme is developed based on Lucas multiwavelet functions and also modified and pseudo\u2010operational matrices. Under suitable properties of these matrices, we present the computational algorithm with high accuracy for solving the proposed problems. Modified and pseudo\u2010operational matrices are employed to achieve the nonlinear algebraic equation corresponding to the proposed problems. In addition, the convergence of the approximate solution to the exact solution is proven by providing an upper bound of error estimate. Numerical experiments for both classes of problems are presented to confirm our theoretical analysis.<\/jats:p>","DOI":"10.1002\/nla.2346","type":"journal-article","created":{"date-parts":[[2020,11,4]],"date-time":"2020-11-04T14:00:39Z","timestamp":1604498439000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A novel direct method based on the Lucas multiwavelet functions for variable\u2010order fractional reaction\u2010diffusion and subdiffusion equations"],"prefix":"10.1002","volume":"28","author":[{"given":"Haniye","family":"Dehestani","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences Alzahra University Tehran Iran"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-5167-6874","authenticated-orcid":false,"given":"Yadollah","family":"Ordokhani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematical Sciences Alzahra University Tehran Iran"}]},{"given":"Mohsen","family":"Razzaghi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics Mississippi State University Starkville Mississippi USA"}]}],"member":"311","published-online":{"date-parts":[[2020,11,4]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/andp.200310032"},{"key":"e_1_2_11_3_1","volume-title":"Initialization, conceptualization, and application in the generalized fractional calculus","author":"Lorenzo C","year":"1998"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-008-9385-8"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1002\/andp.200710246"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-016-2916-9"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.1177\/1077546307087437"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2004.06.029"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2016.07.010"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1177\/1077546315586646"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1002\/mma.5840"},{"key":"e_1_2_11_12_1","first-page":"1","article-title":"Pseudo\u2010operational matrix method for the solution of variable\u2010order fractional partial integro\u2010differential equations","author":"Dehestani H","year":"2020","journal-title":"Eng Comput"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1002\/num.22233"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(85)90028-7"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(92)90441-R"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0301-0104(02)00714-0"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0378-4371(99)00469-0"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.memsci.2008.04.028"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.81.031115"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.77.021111"},{"key":"e_1_2_11_21_1","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-018-1862-x"},{"key":"e_1_2_11_22_1","article-title":"A simple numerical method for two\u2010dimensional nonlinear fractional anomalous sub\u2010diffusion equations","author":"Sweilam N","year":"2020","journal-title":"Math Methods Appl Sci"},{"key":"e_1_2_11_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.06.012"},{"issue":"6","key":"e_1_2_11_24_1","article-title":"Wavelets Galerkin method for the fractional subdiffusion equation","volume":"11","author":"Heydari M","year":"2016","journal-title":"J Comput Nonlinear Dyn"},{"key":"e_1_2_11_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2016.08.028"},{"key":"e_1_2_11_26_1","article-title":"Fractional\u2010Lucas optimization method for evaluating the approximate solution of the multi\u2010dimensional fractional differential equations","author":"Dehestani H","year":"2021","journal-title":"Eng Comput"},{"key":"e_1_2_11_27_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2017.07.046"},{"key":"e_1_2_11_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.09.006"},{"key":"e_1_2_11_29_1","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2259"},{"key":"e_1_2_11_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.01.063"},{"key":"e_1_2_11_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.08.034"},{"key":"e_1_2_11_32_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-018-0171-4"},{"key":"e_1_2_11_33_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.04.019"},{"key":"e_1_2_11_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2018.09.004"},{"key":"e_1_2_11_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2016.12.022"},{"key":"e_1_2_11_36_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.02.050"},{"key":"e_1_2_11_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apnum.2018.11.014"},{"key":"e_1_2_11_38_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.11.020"},{"key":"e_1_2_11_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2011.02.045"},{"key":"e_1_2_11_40_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2018.04.018"},{"key":"e_1_2_11_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2020.113070"},{"key":"e_1_2_11_42_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.05.017"},{"key":"e_1_2_11_43_1","doi-asserted-by":"publisher","DOI":"10.1002\/9781118033067"},{"key":"e_1_2_11_44_1","first-page":"16","article-title":"Expansion of analytic functions in polynomials associated with fibonacci numbers","volume":"1","author":"Byrd PF","year":"1963","journal-title":"Fibonacci Quart"},{"key":"e_1_2_11_45_1","doi-asserted-by":"publisher","DOI":"10.1137\/090771715"},{"key":"e_1_2_11_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.08.012"},{"key":"e_1_2_11_47_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-012-9622-6"}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2346","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/nla.2346","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.2346","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,2]],"date-time":"2023-09-02T06:44:05Z","timestamp":1693637045000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.2346"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,4]]},"references-count":46,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["10.1002\/nla.2346"],"URL":"https:\/\/doi.org\/10.1002\/nla.2346","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,4]]},"assertion":[{"value":"2020-02-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-10-12","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-11-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}