Abstract

In this paper, we study a Cauchy-type problem for one ordinary fractional differential equation with a fractional derivative of Riemann–Liouville in the main part. To achieve this objective, a generalized polynomial projection method based on two pairs of spaces of the required elements and the right parts of its correct statement is proposed and its theoretical and functional justification is given. Using the obtained general results, the convergence of the ‘‘polynomial’’ Galerkin, collocation and subdomains methods of the solution of the corresponding Cauchy type problem is derived.

中文翻译：

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一类分数阶微分方程多项式投影方法的收敛性

摘要

在本文中，我们研究了一个主要分数为Riemann-Liouville的分数导数的常微分方程的Cauchy型问题。为了达到这个目的，提出了一种基于两对所需元素的空间及其正确说明的正确部分的广义多项式投影方法，并给出了理论和功能上的证明。利用获得的一般结果，推导了相应的柯西类型问题解的“多项式” Galerkin的收敛性，搭配和子域方法。