4.6 Article

Existence and stability results for ψ-Hilfer fractional integro-differential equation with mixed nonlocal boundary conditions

Journal

AIMS MATHEMATICS
Volume 6, Issue 4, Pages 4119-4141

Publisher

AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2021244

Keywords

existence; uniqueness; psi-Hilfer fractional derivative; nonlocal boundary condition

Funding

  1. King Mongkut's University of Technology North Bangkok
  2. Center of Excellence in Mathematics (CEM), CHE, Sri Ayutthaya Rd., Bangkok, Thailand
  3. Barapha University

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This paper discusses the existence, uniqueness, and stability of boundary value problems for psi-Hilfer fractional integro-differential equations with mixed nonlocal boundary conditions. The uniqueness result is proved using Banach's contraction mapping principle, and the existence results are established using the Krasnosel'skii's fixed point theorem and the Leray-Schauder nonlinear alternative. Further, four different types of Ulam's stability are studied, and some examples are provided to demonstrate the application of the main results.
In this paper, we discuss the existence, uniqueness and stability of boundary value problems for psi-Hilfer fractional integro-differential equations with mixed nonlocal (multi-point, fractional derivative multi-order and fractional integral multi-order) boundary conditions. The uniqueness result is proved via Banach's contraction mapping principle and the existence results are established by using the Krasnosel' skii's fixed point theorem and the Larey-Schauder nonlinear alternative. Further, by using the techniques of nonlinear functional analysis, we study four different types of Ulam's stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability. Some examples are also constructed to demonstrate the application of main results.

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