Ulam Stability for Nonlinear Fractional Differential Equations with Multi-Term and Nonlocal Multi-Point Boundary Value Problem

Abstract

We focus on Ulam type stability for fractional differential equations with nonlocal multi-point and multi-term boundary conditions. The application of Ulam stability to any type of boundary condition causes some misunderstandings which are mainly connected with the solutions of the applied inequality and the corresponding boundary condition. The main idea of Ulam type stability is the closeness between any solution of the corresponding differential inequality and the solution of the studied problem. Also, both solutions have to be deeply connected. To avoid misunderstandings in the literature we suggest three different approaches. In all of them we study the appropriately defined Ulam type stability.