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

Advances in Difference Equations

article

Ben Chikh, Salim¹  Amara, Abdelkader¹  Etemad, Sina²  Rezapour, Shahram³ 

[1] Laboratory of Applied Mathematics, University of Kasdi Merbah;Department of Mathematics, Azarbaijan Shahid Madani University;Institute of Research and Development, Duy Tan University;Faculty of Natural Sciences, Duy Tan University;Department of Medical Research, China Medical University Hospital, China Medical University

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

DOI  :  10.1186/s13662-020-03012-1

学科分类：航空航天科学

来源: SpringerOpen

【 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