Kamal transform and Ulam stability of φth order linear differential equations

In this manuscript, we discusses the Kamal transform for homogeneous and non-homogeneous linear differential equations. Using this unique integral transform, we resolve higher-order linear differential equations. Alternatively, it can produce the conditions required for Hyers-Ulam stability by using the Kamal transform. This is the first attempt to use the Kamal transform to show that a linear differential equation is stable. The Kamal transform method is more useful for investigating the stability problem for differential equations with constant coefficients, as this study also shows. The discussion of applications follows to illustrate our approach. In other words, we establish sufficient with a constant coefficient by using the Kamal transform method. Moreover, this paper provides a new method to investigate the stability of differential equations. Further, this paper shows that the Kamal transform method is more convenient for investigating stability problems for linear differential equations with a constant coefficient.