Generalized Polynomial Method for Solving a Cauchy-Type Problem for one Fractional Differential Equation

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 that are summable with an arbitrarily fixed degree, we propose a family of pairs of spaces of elements and...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 275; no. 5; pp. 602 - 612
Main Authors Agachev, Yu. R., Guskova, A. V.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Springer
Springer Nature B.V
Subjects
Analysis
Collocation methods
Differential equations
Fractional calculus
Galerkin method
Mathematical analysis
Mathematics
Mathematics and Statistics
Methods
Polynomials
34B05
differential equation
65L03
convergence
Lebesgue space
fractional derivative
well-posed problem
projection method
Cauchy-type problem
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Summary: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 that are summable with an arbitrarily fixed degree, we propose a family of pairs of spaces of elements and right-hand sides that provide the well-posed statement of the problem. 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06701-w