Ulam–Hyers stability of impulsive integrodifferential equations with Riemann–Liouville boundary conditions

Advances in Difference Equations

article

Zada, Akbar¹  Alzabut, Jehad²  Waheed, Hira¹  Popa, Ioan-Lucian³ 

[1] Department of Mathematics, University of Peshawar;Department of Mathematics and General Sciences, Prince Sultan University;Department of Exact Science and Engineering, “1 Decembrie 1918” University of Alba Iulia

关键词: Caputo derivative;    Riemann–Liouville integral;    Impulse;    Ulam–Hyers stability;    Fixed point theory;   

DOI  :  10.1186/s13662-020-2534-1

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

This paper is concerned with a class of impulsive implicit fractional integrodifferential equations having the boundary value problem with mixed Riemann–Liouville fractional integral boundary conditions. We establish some existence and uniqueness results for the given problem by applying the tools of fixed point theory. Furthermore, we investigate different kinds of stability such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. Finally, we give two examples to demonstrate the validity of main results.

【 授权许可】

CC BY