AIMS Mathematics (May 2023)

A coupled system of p-Laplacian implicit fractional differential equations depending on boundary conditions of integral type

  • Dongming Nie,
  • Usman Riaz,
  • Sumbel Begum,
  • Akbar Zada

DOI
https://doi.org/10.3934/math.2023839
Journal volume & issue
Vol. 8, no. 7
pp. 16417 – 16445

Abstract

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The objective of this article is to investigate a coupled implicit Caputo fractional $ p $-Laplacian system, depending on boundary conditions of integral type, by the substitution method. The Avery-Peterson fixed point theorem is utilized for finding at least three solutions of the proposed coupled system. Furthermore, different types of Ulam stability, i.e., Hyers-Ulam stability, generalized Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability, are achieved. Finally, an example is provided to authenticate the theoretical result.

Keywords