Parameter-dependent fractional boundary value problems: analysis and approximation of solutions

Kateryna Marynets*, Dona Pantova

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We study a parameter-dependent non-linear fractional differential equation, subject to Dirichlet boundary conditions. Using the fixed point theory, we restrict the parameter values to secure the existence and uniqueness of solutions, and analyse the monotonicity behaviour of the solutions. Additionally, we apply a numerical-analytic technique, coupled with the lower and upper solutions method, to construct a sequence of approximations to the boundary value problem and give conditions for its monotonicity. The theoretical results are confirmed by an example of the Antarctic Circumpolar Current equation in the fractional setting.

Original languageEnglish
Number of pages21
JournalApplicable Analysis
DOIs
Publication statusPublished - 2024

Keywords

  • approximation of solutions
  • Caputo fractional differential equations
  • fixed-point theorem
  • fractional geophysical model
  • upper and lower solutions

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