On the Convergence of a Polynomial Projection Methods for One Class of Fractional Differential Equations

Abstract

© 2020, Pleiades Publishing, Ltd. 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.