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.

Oceanic Shallow-Water Investigations on a Variable-Coefficient Davey–Stewartson System

“…Based on finding rational solutions f and g, we can obtain the rogue wave solutions of Equation (3).…”

“…The solutions and properties of differential equations are significant [1,2]. For example, the stability of a differential equation not only reflects the characteristics of the equation itself, it plays a role in practical model analysis [3][4][5][6]. Differential equations can be divided into linear equations and nonlinear equations.…”

Integral Transforms and the Hyers–Ulam Stability of Linear Differential Equations with Constant Coefficients

“…The first paper of this type is by Rezaei, Jung, and Rassias [1] using the Laplace transform; other papers using the Laplace transform to investigate Hyers-Ulam stability include [2,3]. Since then, scholars have used a variety of integral transform definitions to explore Hyers-Ulam stability, including the Kamal [4], Mahgoub [5][6][7][8], Tarig [9], Shehu [10], Sawi [11], Aboodh [12][13][14], Fourier [15][16][17][18], general [19], and Elzaki [20] integral transforms. Fourier transforms require functions and equations to be defined on the whole real line (−∞, ∞), while the other transforms listed above require functions and equations to be defined on the half-line [0, ∞).…”