文章基本信息

标题：Modelling of the Convection-Diffusion Equation through Fractional Restricted Calculus of Variations. ⁎ ⁎
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作者：Jacky Cresson ; Fernando Jiménez ; Sina Ober-Blöbaum 等
期刊名称：IFAC PapersOnLine
印刷版ISSN：2405-8963
出版年度：2021
卷号：54
期号：9
页码：482-487
DOI：10.1016/j.ifacol.2021.06.105
语种：English
出版社：Elsevier
摘要：AbstractWe deliver a restricted variational principle that provides, after the application of the Hamilton’s principle, a particular set of α-fractional PDEs as sufficient condition for the extremals when it is applied over a given action. This action is defined as the integral of a particular Lagrangian function containing the fractional derivatives (both for space and time variables) of the involved scalar fields as part of the state space. We see that the convection-difussion equation is a particular instance of these α-fractional PDEs, say whenα =1/2. Furthermore, we briefly explore some paths towards discretisation of the restricted variational principle and the fractional PDEs. It is to be expected that the obtained discrete version of the equations, coming from a variational principle, would inherit some of the geometric/preservation properties of their continuous counterparts. This is left as subject of future study.
关键词：KeywordsConvection-diffusion equationFractional derivativesPDEsHamilton’s principleRestricted variational principleDiscretisationVariational integrators