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

Abstract

Abstract 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.

Keywords

• Boundary value problem
• Hyers–Ulam stability
• Multi-order fractional differential equation
• Riemann–Liouville derivative