Ulam–Hyers Stability of Linear Differential Equation with General Transform

Abstract

The main aim of this study is to implement the general integral transform technique to determine Ulam-type stability and Ulam–Hyers–Mittag–Leffer stability. We are given suitable examples to validate and support the theoretical results. As an application, the general integral transform is used to find Ulam stability of differential equations arising in Thevenin equivalent electrical circuit system. The results are graphically represented, which provides a clear and thorough explanation of the suggested method.

Keywords

• general integral transform
• linear differential equation
• Thevenin equivalent electrical circuit
• Ulam–Hyers and Ulam–Hyers <i>ϕ</i>-stability