A regularization method for Caputo fractional derivatives in the Banach space L[0 , T]

Nguyen Van Duc, Thi Phong Nguyen

Research output: Contribution to journalArticlepeer-review

Abstract

This work is dedicated to the investigation of a regularization method for the problem of determining Caputo fractional derivatives of a function in the Banach space L[0 , T] . This regularization method is based on the approximation of the first-order derivative of the function by the solution of a well-posed problem depending on a regularization parameter. We then discuss the Hölder type stability results for the method according to two choice rules for the regularization parameter, which are an a priori parameter choice rule and an a posteriori parameter choice rule. Some numerical examples are provided.

Original languageEnglish (US)
Pages (from-to)1033-1053
Number of pages21
JournalNumerical Algorithms
Volume95
Issue number2
DOIs
StatePublished - Feb 2024

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

  • A posteriori parameter choice rules
  • A priori parameter choice rule
  • Caputo fractional derivative
  • Error estimates
  • Ill-posed problems
  • Regularization

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