Abstract

In this paper we focus on Ulam type stability for a class of nonlocal boundary value problems containing multi-term delay fractional differential equations and nonlocal multi-point and multi-strip boundary conditions. The application of Ulam stability to any type of boundary conditions causes some misunderstandings which are mainly connected with the solutions of the applied inequality and the corresponding boundary condition. If the inequality is not defined in an appropriate way, then its solutions could not satisfy the boundary condition and the corresponding integral presentation is not valid. In this paper we suggest some ways to avoid these misunderstandings. In one of them we consider a fractional integral inequality. In the second one we suggest a fractional differential inequality with a boundary condition. In both cases we slightly change the classical definition of Ulam stability. In the last way we consider a parameter in the boundary condition and a fractional differential inequality. This parameter depends significantly on the chosen solution of the fractional differential inequality. We illustrate the three suggested approaches only on Ulam-Hyers stability and generalized Ulam-Hyers stability with appropriate changes of the classical definitions. The same approaches could be applied similarly to other types of stability such as Ulam-Hyers-Rassias stability, generalized Ulam-Hyers-Rassias stability.

Keywords: Caputo; delay differential equations; multi-term; nonlocal multi-point integral boundary conditions; Ulam stability.

MSC: 34A34, 34A08, 34D20

DOI: 10.57016/MV-P55yXA83

Pages:  1--15