Abstract
In this paper, we study the existence and uniqueness of solution for fractional differential equations with mixed fractional derivatives, integrals and multi-point conditions. After that, we also establish different kinds of Ulam stability for the problem at hand. Examples illustrating our results are also presented.
Highlights
Fractional differential equations has proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos
Fractional differential equations has found its applications in many real world phenomena and process of dynamics, biology, signal and image processing, cosmology, physics, chemistry, etc
One important and interesting area of research of fractional differential equations is devoted to the stability analysis
Summary
Fractional differential equations has proved to be an important tool in the modelling of dynamical systems associated with phenomena such as fractal and chaos. There have been few works considering the Ulam stability of variety of classes of fractional differential equations [26,27,28,29,30]. In this paper, motivated by the papers [26,27,28,29,30] we investigate the existence, uniqueness and Ulam stability such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability for fractional differential equations with more general nonlocal boundary conditions. Mathematics 2019, 7, 117 where u ∈ C1 ([0, T ], R) is a continuous function, c D α , c D β j denote the Caputo fractional derivative of orders α and β j , respectively, 0 < β j < α ≤ 1 for j = 1, 2, . We emphasize that (1) is a multi-point, fractional derivative multi-order and fractional integral multi-order problem.
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