Ulam–Hyers Stability and Simulation of a Delayed Fractional Differential Equation with Riemann–Stieltjes Integral Boundary Conditions and Fractional Impulses

Abstract

In this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficient assessments for convenient verification have been devised to ensure the existence and uniqueness of solutions. We further employ the nonlinear analysis to reveal that this problem is Ulam–Hyers (UH) stable. Finally, some examples and numerical simulations are presented to illustrate the reliability and validity of our main results.

Keywords

• fractional-order impulses
• Riemann–Stieltjes integral
• fixed-point theorem
• UH-stability