Approximation Approach to the Fractional BVP with the Dirichlet Type Boundary Conditions

Kateryna Marynets*, Dona Pantova

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
35 Downloads (Pure)

Abstract

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.

Original languageEnglish
Number of pages20
JournalDifferential Equations and Dynamical Systems
DOIs
Publication statusPublished - 2022

Keywords

  • Approximation of solutions
  • Brouwer degree
  • Dirichlet boundary conditions
  • Fractional differential equations

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