On Hyers–Ulam stability of a multi-order boundary value problems via Riemann–Liouville derivatives and integrals

Advances in Difference Equations

Sina Etemad¹  Shahram Rezapour²  Salim Ben Chikh³  Abdelkader Amara³ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran;Institute of Research and Development, Duy Tan University, 550000, Da Nang, Vietnam;Faculty of Natural Sciences, Duy Tan University, 550000, Da Nang, Vietnam;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;Laboratory of Applied Mathematics, University of Kasdi Merbah, 30000, Ouargla, Algeria;

关键词: Boundary value problem;    Hyers–Ulam stability;    Multi-order fractional differential equation;    Riemann–Liouville derivative;    34A08;    34A12;   

DOI  :  10.1186/s13662-020-03012-1

来源: Springer

【 摘 要 】

In this research paper, we introduce a general structure of a fractional boundary value problem in which a 2-term fractional differential equation has a fractional bi-order setting of Riemann–Liouville type. Moreover, we consider the boundary conditions of the proposed problem as mixed Riemann–Liouville integro-derivative conditions with four different orders which cover many special cases studied before. In the first step, we investigate the existence and uniqueness of solutions for the given multi-order boundary value problem, and then the Hyers–Ulam stability is another notion in this regard which we study. Finally, we provide two illustrative examples to support our theoretical findings.

【 授权许可】

CC BY