Ulam–Hyers Stability and Uniqueness for Nonlinear Sequential Fractional Differential Equations Involving Integral Boundary Conditions

• Published in: Fractal and fractional 2021-12, Vol.5 (4), p.235
• Main Authors: Al-khateeb, Areen, Zureigat, Hamzeh, Ala’yed, Osama, Bawaneh, Sameer
• Format: Article
• Language: English
• Subjects: Boundary conditions; Boundary value problems; Calculus; Differential equations; fixed-point theorem; fractional differential equation; Mathematical models; sequential fractional differential equation; Stability; Ulam–Hyers stability; Uniqueness
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract5040235

Fractional-order boundary value problems are used to model certain phenomena in chemistry, physics, biology, and engineering. However, some of these models do not meet the existence and uniqueness required in the mainstream of mathematical processes. Therefore, in this paper, the existence, stability, and uniqueness for the solution of the coupled system of the Caputo-type sequential fractional differential equation, involving integral boundary conditions, was discussed, and investigated. Leray–Schauder’s alternative was applied to derive the existence of the solution, while Banach’s contraction principle was used to examine the uniqueness of the solution. Moreover, Ulam–Hyers stability of the presented system was investigated. It was found that the theoretical-related aspects (existence, uniqueness, and stability) that were examined for the governing system were satisfactory. Finally, an example was given to illustrate and examine certain related aspects.