Approximation approach to the fractional BVP with the Dirichlet type boundary conditions

We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the...

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Bibliographic Details
Published inarXiv.org
Main Authors Marynets, Kateryna, Pantova, Dona
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 31.01.2022
Subjects
Approximation
Boundary conditions
Boundary value problems
Computer Science - Numerical Analysis
Differential equations
Dirichlet problem
Mathematics - Numerical Analysis
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Summary:We use a numerical-analytic technique to construct a sequence of successive approximations to the solution of a system of fractional differential equations, subject to Dirichlet boundary conditions. We prove the uniform convergence of the sequence of approximations to a limit function, which is the unique solution to the boundary value problem under consideration, and give necessary and sufficient conditions for the existence of solutions. The obtained theoretical results are confirmed by a model example.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.2201.08638