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

• Main Authors: Weerawat Sudsutad, Chatthai Thaiprayoon, Sotiris K. Ntouyas
• Format: Article
• Language: English
• Published: AIMS Press 2021-02-01
• Series: AIMS Mathematics
• Subjects: existence; uniqueness; ψ-hilfer fractional derivative; nonlocal boundary condition
• Online Access: http://www.aimspress.com/article/doi/10.3934/math.2021244?viewType=HTML

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'ski\u{i}'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, \emph{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.