伽辽金法
数学
趋同(经济学)
应用数学
分数阶微积分
数学分析
物理
有限元法
经济
热力学
经济增长
出处
期刊:Fractional Calculus and Applied Analysis
[De Gruyter]
日期:2024-05-06
被引量:1
标识
DOI:10.1007/s13540-024-00287-z
摘要
In the context of forward uncertainty quantification, we investigate the convergence of the Galerkin projections for random fractional differential equations. The governing system is formed by a finite set of independent input random parameters (a germ) and by a fractional derivative in the Caputo sense. Input uncertainty arises from biased measurements, and a fractional derivative, defined by a convolution, takes past history into account. While numerical experiments on the gPC-based Galerkin method are already available in the literature for random ordinary, partial and fractional differential equations, a theoretical analysis of mean-square convergence is still lacking for the fractional case. The aim of this contribution is to fill this gap, by establishing new inequalities and results and by raising new open problems.
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