Abstract:
In this paper, we examine a Cauchy-type problem for one ordinary differential equation with Riemann–Liouville fractional derivatives. For this problem, based on the Lebesgue space of functions summable with an arbitrarily fixed degree, we propose a family of pairs of spaces of elements and right-hand sides that yield its well-posed statement. In these pairs of spaces, we develop a generalized polynomial projection method for solving the problem considered and justify it from the functional-theoretic point of view. Based on the general results obtained, we prove the convergence of the “polynomial” Galerkin method, the collocation method, and the subdomain method for solving the corresponding Cauchy-type problem.
Citation:
Yu. R. Agachev, A. V. Guskova, “Generalized polynomial method for solving a Cauchy-type problem for one fractional differential equation”, Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 2, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 176, VINITI, Moscow, 2020, 80–90
\Bibitem{AgaGus20}
\by Yu.~R.~Agachev, A.~V.~Guskova
\paper Generalized polynomial method for solving a Cauchy-type problem for one fractional differential equation
\inbook Proceedings of the XVII All-Russian Youth School-Conference «Lobachevsky Readings-2018»,
November 23-28, 2018, Kazan. Part 2
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2020
\vol 176
\pages 80--90
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into589}
\crossref{https://doi.org/10.36535/0233-6723-2020-176-80-90}
Linking options:
https://www.mathnet.ru/eng/into589
https://www.mathnet.ru/eng/into/v176/p80
This publication is cited in the following 1 articles:
A. I. Fedotov, “Substantiation of a quadrature-difference method for solving integro-differential equations with derivatives of variable order”, Comput. Math. Math. Phys., 62:4 (2022), 548–563
Citation in format AMSBIB
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