Stability analysis of multi-point boundary conditions for fractional differential equation with non-instantaneous integral impulse

• Published in: Mathematical biosciences and engineering : MBE Vol. 20; no. 4; pp. 7020 - 7041
• Main Authors: Li, Guodong, Zhang, Ying, Guan, Yajuan, Li, Wenjie
• Format: Journal Article
• Language: English
• Published: United States AIMS Press 01-01-2023
• Subjects: caputo fractional derivative; existence; multi-point boundary conditions; non-instantaneous integral impulse; stability; existence; multi-point boundary conditions; Caputo fractional derivative; stability; non-instantaneous integral impulse
• ISSN: 1551-0018; 1551-0018
• DOI: 10.3934/mbe.2023303

This paper considers the stability of a fractional differential equation with multi-point boundary conditions and non-instantaneous integral impulse. Some sufficient conditions for the existence, uniqueness and at least one solution of the aforementioned equation are studied by using the Diaz-Margolis fixed point theorem. Secondly, the Ulam stability of the equation is also discussed. Lastly, we give one example to support our main results. It is worth pointing out that these two non-instantaneous integral impulse and multi-point boundary conditions factors are simultaneously considered in the fractional differential equations studied for the first time.