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

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.

Automated summary

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.