Fractional periodic boundary value and Cauchy problems with Hilfer–Prabhakar operator

Kateryna Marynets*, Živorad Tomovski

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

We introduce a successive approximations method to study one fractional periodic boundary value problem of the Hilfer-Prabhakar type. The problem is associated to the corresponding Cauchy problem, whose solution depends on an unknown initial value. To find this value we numerically solve the so-called ’determining system’ of algebraic or transcendental equations. As a result, we determine an approximate solution of the studied problem, written in a closed form. Finally, we evaluate efficiency of our method on a nonlinear numerical example.

Original languageEnglish
Article number130
Number of pages20
JournalComputational and Applied Mathematics
Volume43
Issue number3
DOIs
Publication statusPublished - 2024

Keywords

  • Cauchy problem
  • Determining system
  • Hilfer–Prabhakar fractional derivative
  • Periodic boundary conditions
  • Successive approximations

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