Boundary Value Problems (Oct 2024)

Analysis of Caputo fractional variable order multi-point initial value problems: existence, uniqueness, and stability

  • Hicham Ait Mohammed,
  • Mohammed El-Hadi Mezabia,
  • Brahim Tellab,
  • Abdelkader Amara,
  • Homan Emadifar

DOI
https://doi.org/10.1186/s13661-024-01943-2
Journal volume & issue
Vol. 2024, no. 1
pp. 1 – 28

Abstract

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Abstract In this paper, we examine the existence, uniqueness, and stability of solutions for a Caputo variable order ϑ-initial value problem (ϑ-IVP) with multi-point initial conditions. The proofs for uniqueness and existence leverage Sadovski’s and Banach’s fixed point theorems, along with the Kuratowski measure of noncompactness. Furthermore, we explore the Ulam–Hyers–Rassias (UHR) stability of the solution. To validate our findings, we present a numerical example.

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